CN102231099B - Method for correcting per-pixel response brightness in multi-projector auto-stereoscopic display - Google Patents

Abstract

The invention discloses a method for correcting per-pixel response brightness in multi-projector auto-stereoscopic display, which belongs to the technical field of large-screen high-resolution display in multi-projector combination display. The method is characterized by comprising the following steps of: taking projections of all projectors corresponding to the same viewpoint image after geometries and brightness are corrected as a projection of a virtual projector; measuring a brightness response function of each point in the virtual projector; and according to different brightness response functions of each point, pre-converting the brightness of an input image, wherein the problem of inconsistent brightness in the whole display region resulted from the conjoining display of each viewpoint image in a multi-projector auto-stereoscopic display system through a plurality of projectors can be resolved; consistent seamless conjoining large-screen high-resolution display brightness of each viewpoint image in the multi-projector auto-stereoscopic display system is realized; according to the method, the problem of different brightness response functions of each point on the screen in the multi-projector auto-stereoscopic display system resulted from specific optical properties of the screen can be resolved; and the brightness correction result is more uniform and consistent.

Description

The brightness correcting method by pixel response that multi-projector free stereo shows

Technical field

The present invention relates to multi-projector free stereo show combination show, realize multi-projector free stereo show giant-screen high resolving power show brightness consistent.

Background technology

In recent years, the stereoscopic vision based on binocular parallax is widely used in the every field such as film, game, emulation, virtual reality.Now, free 3 D display technology has also been obtained major technological breakthrough, and it makes beholder just can see (right and left eyes) image corresponding to different points of view by eyes without wearing anaglyph spectacles, thereby produces strong three-dimensional stereoscopic visual effect.Current auto-stereoscopic display is subject to the restrictions such as the resolution of individual monitor, can only hold less spectators to watch in the region of certain appointment, and this has limited its promotion and application.Multiple visual point images are shown and can effectively be addressed the above problem with the combination that multiple projector carry out free stereo demonstration.But the screen characteristic that multi-projector free stereo shows makes geometry correction and brightness correcting method that conventional combination shows be difficult to application.Traditional brightness correcting method mainly comprises brightness fusion method and brightness decay method.

Brightness fusion method utilizes projector space that geometry correction obtains and the coordinate transformation relation of screen space to calculate the overlapping view field in projector space, and in the overlapping region in projector space, calculate from 0 to the 1 brightness decay factor of transition gradually, making the brightness decay factor sum of all projector that every bit on screen space is corresponding is 1.Brightness fusion method is simple and be easy to calculating, but can only solve the luminance difference of projector overlapping region, and the luminance difference between projector inside and projector is ignored.

Brightness decay method is carried out gamma correction by intensity transfer function and maximum, the minimum brightness response curved surface of measuring each projector.The method is only measured an intensity transfer function to each projector.In multi-projector auto-stereo display system, adopt special optical screen in order to obtain free stereo display effect.The special optical character of these screens has caused the intensity transfer function each point difference of projector.So, in multi-projector auto-stereo display system, apply brightness decay method and carry out gamma correction and can not obtain good gamma correction effect.

Summary of the invention

The object of the invention is to solve the brightness inconsistence problems that in multi-projector auto-stereo display system, each visual point image is shown the whole viewing area of causing with multiple projector splicings, realized the brightness that in multi-projector auto-stereo display system, the seamless spliced giant-screen high resolving power of each visual point image shows consistent.

The invention is characterized in, contain successively following steps:

Step (1): set up a variable resolution multi-projector auto-stereo display system that there is viewpoint and count two visual point images of I=2, comprise: an array of rear-projectors, an auto-stereoscopic display screen curtain, be called for short screen, a digital camera, a server and multiple client computer below, wherein, array of rear-projectors is made up of 24 DLP projector, each visual point image is pressed the mode tiled display of the capable Nc row of Nr on auto-stereoscopic display screen curtain with Nr × Nc DLP projector, Nr=3, Nc=4; Client computer has 12, two described DLP projector of every client computer control;

Step (2): described server carries out geometry correction to described multi-projector auto-stereo display system, and step is as follows:

Step (2.1): show respectively in the projector space of each projector frame buffer by each client by the image of the unique point composition of the equidistant distribution of setting, form projector space initial mesh meshp _ij, i represents the sequence number of viewpoint, i=1, and 2, j represents the sequence number of corresponding described DLP projector in each viewpoint i, j=1,2 ..., 11,12; Obtain respectively with described digital camera the screen characteristics dot image that the unique point image projection of corresponding each the described DLP projector of each viewpoint forms on described screen again, form the initial mesh meshd of screen space _ij;

Step (2.2): be calculated as follows in i viewpoint the correcting area dispW of j projector on described screen _ij,

dispW _ij=∩(dispA _ij,rect)，i=0,1，j=1,2,…,11,12 （1）

Wherein, dispA _ijbe j projector viewing area on screen in i viewpoint, rect is the region that on described screen, combination shows,

$\mathrm{rect}={\∩}_{i=1}^{\mathrm{Nv}}\left(\mathrm{inrect}\left({\∪}_{j=1}^{\mathrm{Nr}\×\mathrm{Nc}}\mathrm{disp}{A}_{\mathrm{ij}}\right)\right)---\left(2\right)$

In i viewpoint, the summation of totally 12 DLP projector viewing areas on described screen is used

dispA _ijrepresent, mono-of inrect asks the function that connects rectangle in given area;

Step (2.3): j the correcting area dispW that DLP projector shows on described screen in i viewpoint _ijin regenerate by the unique point of described equidistant setting and be organized into described correcting area dispW _ijat the calibration grid meshnd of described screen space _ij; Again according to the calibration grid meshnd of described screen space _ijthe coordinate (D of summit D _u,, D _v) calculate its corresponding projector free-air correction grid meshnp _ijpoint D ' coordinate (D ' _x, D ' _y);

As the calibration grid meshnd of described screen space _ijsummit D(D _u, D _v) area coordinate while being (m, k, w),

$m=\frac{S\left(\mathrm{\ΔABD}\right)}{S\left(\mathrm{\ΔABC}\right)}=\frac{\left|\begin{array}{ccc}{A}_u& B_u& D_u\\ A_v& B_v& D_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},$ $k=\frac{S\left(\mathrm{\ΔDBC}\right)}{S\left(\mathrm{\ΔABC}\right)}=\frac{\left|\begin{array}{ccc}{D}_u& B_u& C_u\\ D_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},$ $w=\frac{S\left(\mathrm{\ΔADC}\right)}{S\left(\mathrm{\ΔABC}\right)}=\frac{\left|\begin{array}{ccc}{A}_u& D_u& C_u\\ A_v& D_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_v& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}---\left(3\right)$

Wherein, Δ ABC is that D point is at described initial mesh meshd _ijthe triangle at middle place, m is the interior triangle Δ ABD of Δ ABC and the ratio of the area of this triangle Δ ABC, k is the interior triangle Δ DBC of Δ ABC and the ratio of the area of this triangle Δ ABC, and w is the interior triangle Δ ADC of Δ ABC and the ratio of the area of this triangle Δ ABC, (A _u, A _v), (B _u, B _v) and (C _u, C _v) be three apex coordinates of Δ ABC;

Described projector free-air correction grid meshnp _ijpoint D ' coordinate (D ' _x, D ' _y) be

$\left\{\begin{array}{c}{D}_x^{\′}=m\×A_x^{\′}+k\×B_x^{\′}+w\×C_x^{\′}\\ D_y^{\′}=m\×A_y^{\′}+k\×B_y^{\′}+w\×C_y^{\′}\end{array}\right.---\left(4\right)$

Wherein, Δ A ' B ' C ' is at described grid meshp _ijin with described grid meshd _ijthe corresponding triangle of Δ ABC, three apex coordinates of Δ A ' B ' C ' be respectively (A ' _x, A ' _y), (B ' _x, B ' _y), (C ' _x, C ' _y);

Step (2.4): the calibration grid meshnp that is calculated as follows described server and distributes to by each client j DLP projector in i viewpoint _ijthe reference position (x of image ^ij _start, y ^ij _start), wide high width _ijand height _ij, and distribute to described calibration grid meshnp _ijthe texture coordinate (xx on e summit _ije, yy _ije);

$\left\{\begin{array}{c}{x^{\mathrm{ij}}}_{\mathrm{start}}=[({u^{\mathrm{ij}}}_{\min }-u_{\min })/(u_{\max }-u_{\min })]\×\mathrm{wd}\\ {y^{\mathrm{ij}}}_{\mathrm{start}}=[({v^{\mathrm{ij}}}_{\min }-v_{\min })/(v_{\max }-v_{\min })]\×\mathrm{hd}\end{array}\right.---\left(5\right)$

$\left\{\begin{array}{c}{\mathrm{width}}_{\mathrm{ij}}=[({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })/(u_{\max }-u_{\min })]\×\mathrm{wd}\\ {\mathrm{height}}_{\mathrm{ij}}=[{{(v}^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })/(v_{\max }-v_{\min })]\×\mathrm{hd}\end{array}\right.---\left(6\right)$

$\left\{\begin{array}{c}{\mathrm{xx}}_{\mathrm{ije}}=(u_{\mathrm{ije}}-{u^{\mathrm{ij}}}_{\min })/({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })\\ {\mathrm{yy}}_{\mathrm{ije}}=(v_{\mathrm{ije}}-{v^{\mathrm{ij}}}_{\min })/({v^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })\end{array}\right.---\left(7\right)$

Wherein, width _ijand height _ijthe calibration grid meshnp of described server-assignment to j DLP projector in i viewpoint _ijimage wide and high, wd and hd are wide and high before projection of image of wanting tiled display on described screen, (u _min, v _min) and (u _max, v _max) be the apex coordinate that combines the lower left corner and the upper right corner of viewing area rect on described screen, u ^ij _min, u ^ij _max, v ^ij _minand v ^ij _maxrespectively correcting area dispW _ijfour apex coordinates in minimum, the maximal value of minimum, maximal value and ordinate of horizontal ordinate, (u _ije, v _ije) be calibration grid meshnp _ijin the coordinate of screen space of screen corresponding to e summit, i=1,2, j=1,2 ..., Nr*Nc;

Step (2.5): server will combine each client in program every piece image of demonstration, the reference position, the size that calculate by step (2.4) intercept corresponding subimage and distribute to corresponding client computer, to the subimage of distribution is mapped to corresponding geometry correction grid meshnp by the described texture coordinate calculating _ijupper, then export with projector projection, the splicing effect of geometric alignment on described screen, obtained;

Step (3): adopt according to the following steps successively brightness fusion method to carry out transkit attenuation to the brightness at the edge of each DLP projector overlapping region on screen described in described multi-projector auto-stereo display system;

Step (3.1): be calculated as follows the intensity correction values A that the projector space each point (x, y) of j projector in i viewpoint is located _ij(x, y), is combined into the gamma correction template of this j projector:

$A_{\mathrm{ij}}(x,y)={\left(\frac{a_{\mathrm{ij}}(u,v)}{{\mathrm{\Σ}}_{j^{\′}=1}^{\mathrm{Nr}\×\mathrm{Nc}}{a}_{\mathrm{ij}\′}(u,v)}\right)}^{1/\mathrm{\γ}}---\left(8\right)$

Wherein, (u, v) is the screen space coordinates corresponding to projector space (x, y) of j DLP projector of i viewpoint, i=1, and 2, j=1,2 ..., Nr*Nc, γ=2.4, a _ij(u, v) is the correcting area dispW of j projector of i viewpoint _ijmiddle screen space point (u, v) arrives the distance minimum value on its four borders, j '=1, and 2 ..., Nr*Nc, but j ' ≠ j and correcting area dispW _ijwith correcting area dispW _{ij '}there is overlapping region, a _{ij '}(u, v) is the correcting area dispW of i the individual projector of viewpoint j ' _{ij '}middle screen space point (u, v) is to the distance minimum value on its four borders, at Non-overlapping Domain a _{ij '}(u, v)=0;

Step (3.2): reprojection output after the value correspondence of every bit in the value of the every bit of image after projector geometry correction and gamma correction template is multiplied each other, thus the combination that obtains the brightness decay of projector overlapping region shows;

Step (3.3): all DLP projector relevant each viewpoint are carried out to projector image after geometry and the gamma correction projected image as a virtual projection instrument by step (1) and step (2);

Step (4): the irradiance value of calculating according to the following steps successively corresponding each sampling brightness input on each location of pixels of each described virtual projection instrument;

Step (4.1): get K sampled point by certain interval in the interval [0,255] of brightness value, calculate for the ease of storage below, equilibration time and precision, get K=30, is calculated as follows the brightness value SL of 30 sampled points _k,

${\mathrm{SL}}_k=\left\{\begin{array}{cc}8\&times;(k-1)& 1\&le;k\&le;15\\ 8\&times;(k+2)& 15<k\&le;29\\ 255& k=30\end{array}\right.,k=\mathrm{1,2}...k---\left(9\right)$

Step (4.2): generating size is K the image of xRes X yRes, K=30, wherein, xRes=1024, yRes=768; K image I _kin the brightness of every identical, be all k sampling brightness value SL _k, k=1,2 ... K; 0.02s get S time shutter Δ t between 2.0s _s, s=1,2 ..., S, wherein S=16;

Step (4.3): all images to all virtual projection instrument and second step generation repeat following step (4.3.1)～step (4.3.2), obtain the irradiance value of corresponding each sampling brightness input in the each pixel in each virtual projection instrument;

Step (4.3.1): k the image I generating for i the virtual projection instrument step display (4.2) described in step (3.3) _kprojection result on screen is Δ t camera being set respectively to the time shutter _s, s=1,2 ..., S, after take pictures, obtaining the individual size of S ' is the image of xcRes X ycRes, wherein, S '=S, xcRes and ycRes are respectively the wide and high of camera image, xcRes=2288, ycRes=1520;

Step (4.3.2): with setting time shutter Δ t _sthe take pictures brightness value Z of p point in the described image of obtaining step (4.3.1) of camera _psirradiance E with this point _p,

$\ln E_p=\frac{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(Z_{\mathrm{ps}}\right)(g\left(Z_{\mathrm{ps}}\right)-\ln {\mathrm{\&Delta;t}}_s)}{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(Z_{\mathrm{ps}}\right)},p=\mathrm{1,2}...P---\left(10\right)$

Wherein, P is the number of pixels in each image, P=2288*1520, function g (Z _ps) be Z _psand E _pwith Δ t _sthe mapping relations of logarithmic function,

g(Z _ps)=lnE _p+lnΔt _s （11）

W (Z _ps) be to distribute to brightness Z _psweight,

$w\left(Z_{\mathrm{ps}}\right)=\left\{\begin{array}{cc}{Z}_{\mathrm{ps}}-Z_{\min }& Z_{\mathrm{ps}}\&le;Z_{\mathrm{mid}}\\ Z_{\max }-Z_{\mathrm{ps}}& Z_{\mathrm{ps}}>Z_{\mathrm{mid}}\end{array}\right.---\left(12\right)$

Step (4.3.3): in order to obtain exporting one to one with the input position of described virtual projection instrument at screen space, on corresponding each described irradiance image mapped to grid that each described DLP projector is calculated step (4.3.2), and the irradiance image on these grids is superimposed and obtains the output of virtual projection instrument; On grid, the coordinate (x, y) on each summit and texture coordinate (tex_x, tex_y) are respectively

$\left\{\begin{array}{c}x=(D_u-\min x)/(\max x-\min x)*\mathrm{xRes}\\ y=(D_v-\min y)/(\max y-\min y)*\mathrm{yRes}\end{array}\right.---\left(13\right)$

$\left\{\begin{array}{c}\mathrm{tex}\_x=D_u/\mathrm{xcRes}\\ \mathrm{tex}\_y=D_v/\mathrm{ycRes}\end{array}\right.---\left(14\right)$

Wherein, (D _u, D _v) be summit in the calibration grid of the each projector coordinate at screen space, (minx, and (maxx miny), maxy) be respectively the upper left corner of whole correcting area and the lower right corner coordinate at screen space, xRes and yRes divide image wide and high that maybe combine demonstration, and xcRes and ycRes are respectively the wide and high of camera image;

Step (5): generate K some P in each pixel of virtual projection instrument _k, k=0,1 ... K-1, K=30, wherein, k some P _khorizontal ordinate be k+1, this pixel place sampling brightness value, ordinate is the irradiance value that this pixel place calculates the brightness value input of should sampling; In order to obtain the corresponding relation of continuous input and output brightness, calculate being three Uniform B-spline interpolation curves of this K point, and obtain the reference mark of B-spline curves by following formula,

Wherein, V ₀, V ₁..., V _k+1it is reference mark; Solve the tri-diagonal matrix equation in above formula with chasing method, obtain the reference mark V of three Uniform B-spline interpolation curves ₀, V ₁..., V _k+1;

Step (6): in the minimum brightness curved surface that in calculating screen space, vision is consistent, (u, the brightness value of v) locating is any point

$L^{\&prime;}(u,v)=\max (L\min (u,v),\mathrm{\&lambda;}\&times;\frac{|L\min (u,v)-L\min (u^{\&prime;},v^{\&prime;})|}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(16\right)$

Wherein, Lmin (u, v) the sampling brightness SL minimum for virtual projection instrument shows _mingenerate image time corresponding brightness output image in the brightness at (u, v) coordinate place, (u ', v ') is the neighbor point of (u, v), Lmin (u ', v ') shows minimum sampling brightness SL for virtual projection instrument _mingenerate image time corresponding brightness output image in the brightness at (u ', v ') coordinate place, λ is visually-perceptible coefficient, λ=50, max is the function of maximizing;

In the high-high brightness curved surface that in calculating screen space, vision is consistent, (u, the brightness value of v) locating is any point

$L^{\&prime;\&prime;}(u,v)=\min (L\max (u,v),\mathrm{\&lambda;}\&times;\frac{|L\max (u,v)-L\max (u^{\&prime;},v^{\&prime;})}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(17\right)$

Wherein, Lmax (u, v) the sampling brightness SL maximum for virtual projection instrument shows _maxgenerate image time corresponding brightness output image in the brightness at (u, v) coordinate place, (u ', v ') is the neighbor point of (u, v), Lmax (u ', v ') shows maximum sampling brightness SL for virtual projection instrument _maxgenerate image time corresponding brightness output image in the brightness at (u ', v ') coordinate place;

Step (7): the process of this input brightness on corresponding B-spline curves of the brightness calculation of the image that will show of locating according to virtual projection instrument every bit (x, y) according to the following steps is successively as follows:

Step (7.1): the reference mark of the B-spline curves of each location of pixels is packaged into respectively to little texture, by synthetic these an all little textures large reference mark texture; Each B-spline curves are calculated to 32 reference mark; The horizontal ordinate at each reference mark and ordinate account for respectively a passage in texture; For the 2 d texture of 4 passages, the texture size of 32 reference mark needs is 32*2/4=16; For the ease of the calculating of texture coordinate, the mode that little texture is listed as by 4 row 4 is stored; Large texture is stored each little texture by the mode of the capable xRes row of yRes, wherein, and the resolution that xRes*yRes is display device; So the size of large reference mark texture is (xRes*4) * (yRes*4);

Step (7.2): each location of pixels (x, y) at virtual projection instrument is located, repeats step (7.2.1)～step (7.2.4) below, obtains the brightness input after every bit gamma correction; The brightness value of inputting by change, obtains consistent brightness output;

Step (7.2.1): the output brightness scope of this point is compressed to minimum that vision is consistent and high-high brightness curved surface on the interval between the brightness value of this point, obtains the brightness output Wl (x, y) that vision is consistent,

Wl(x,y)=Lmin(x,y)+Ol(x,y)/255.0*(Lmax(x,y)-Lmin(x,y))

（18）

Wherein, Ol (x, y) is the image that will the combine demonstration brightness at this point, the sampling brightness SL that Lmin (x, y) is minimum for virtual projection instrument shows _mingenerate image time corresponding brightness output image in the brightness of this point, Lmax (x, y) is that virtual projection instrument shows maximum sampling brightness SL _maxgenerate image time corresponding brightness output image in the brightness of this point;

Step (7.2.2): the reference mark of three Uniform B-Spline Curves of (x, the y) point obtaining according to previous calculations, calculate two end points P of the c section function of three Uniform B-Spline Curves with following formula _cand P (0) _c(1),

$P_c\left(t\right)=\left[\begin{array}{cccc}1& t& t^2& {\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">t</figure-callout>}}^3\end{array}\right]\frac{1}{6}\left[\begin{array}{cccc}1& 4& 1& 0\\ -3& 0& 3& 0\\ 3& -6& 3& 0\\ -1& 3& -3& 1\end{array}\right]\left[\begin{array}{c}{V}_c\\ V_{c+1}\\ V_{c+2}\\ V_{c+3}\end{array}\right],0\&le;t\&le;1,c=\mathrm{0,1},...,K-1---\left(19\right)$

Wherein, the coefficient parameter that t is B-spline curves, c is the call number of function segment, P _c(t) be each point between the c section function region of B-spline curves, V _c, V _c+1, V _c+2, V _c+3be respectively the call number of B-spline curves for being respectively c, c+1, c+2, the reference mark of c+3; According to these end points P _cand P (0) _c(1), find the call number c between function region, make in interval that Wl (x, y) forms at the ordinate value of two end points of c section function;

Step (7.2.3): calculate (x, y) with dichotomy and put the input brightness Nl (x, y) after gamma correction: be between parametric t original area with [0,1], by getting interval mid point tm, original interval be divided into two; The ordinate E of the point during with formula (19) calculating parameter t=tm on B-spline curves _p; If E _p<Wl (x, y), a half-interval on the Jian Wei left side, new district; If E _p>Wl (x, y) is a half-interval on the right between new district; Constantly interval is divided into two, iteration said process, until interval range is less than the error amount of a setting; Get parametric t for iterating to the interval midrange finally obtaining, calculate the abscissa value of the point on B-spline curves by formula (18), this abscissa value is exactly the input brightness Nl (x, y) that Wl (x, y) is corresponding;

Step (7.2.4): Nl (x, y) is multiplied by the gamma correction template obtaining in step (3), obtains the final brightness input of each projector; The brightness value of inputting by change, obtains consistent brightness output.

The invention has the advantages that, carry out brightness transition according to the intensity transfer function of every bit in projector, solve the different problem of each point intensity transfer function on the screen that the special optical character of screen in multi-projector auto-stereo display system causes, projection using the projection after how much of all projector relevant same visual point image and gamma correction as a virtual projection instrument, accelerate to make the measurements and calculations speed of intensity transfer function to accelerate by B-spline curves matching and GPU, obtain the gamma correction effect of uniformity more.

Brief description of the drawings

Fig. 1 is the schematic diagram of scalable high resolving power multi-projector auto-stereo display system.

Fig. 2 is the initial mesh in projector space.

Fig. 3 is the initial mesh of screen space.

Fig. 4 is the calibration grid of screen space.

Fig. 5 is the calibration grid in projector space.

Fig. 6 is the coordinate conversion in screen space and projector space.

Fig. 7 is the program flow chart of display system.

Embodiment

The present invention is achieved by the following technical programs: with array of rear-projectors, auto-stereoscopic display screen curtain, digital camera, a scalable high resolving power multi-projector auto-stereo display system of server and client side's computing machine composition.Fig. 1 is the schematic diagram of scalable high resolving power multi-projector auto-stereo display system, wherein, and Nv=2, Nr=3, Nc=4.In system, have the image of Nv viewpoint, each visual point image is pressed the mode tiled display of the capable Nc row of Nr on auto-stereoscopic display screen curtain with Nr × Nc DLP projector.Server calculates geometry correction and the brightness correction parameter of each projector, and sends to the client of controlling homolographic projection instrument.Two projector of each client control.The projector that re-sends to its control after the image that the geometry correction that client calculates according to server and the parameter of Fusion Edges will show each width is out of shape carries out projection, thereby on screen, obtains seamless spliced demonstration result.In order to obtain the seamless tiled display of multiple visual point images, first the present invention is used as the projection after a viewpoint relevant all projector geometry corrections and Fusion Edges the projection of a virtual projection instrument; Then, the intensity transfer function of every bit in measurements and calculations virtual projection instrument; Finally, be calculated as and obtained the brightness input that identical brightness output needs according to the intensity transfer function of virtual projection instrument every bit, on giant-screen, obtained brightness by the brightness input of amendment virtual projection instrument consistent.

Due to the anisotropic reflectivity properties of auto-stereoscopic display screen curtain, making screen have high light belt produces, and intensity transfer function each point difference, this makes the brightness decay method of only measuring an intensity transfer function in auto-stereo display system, can not obtain good gamma correction effect.The present invention is by solving the gamma correction problem of multi-projector auto-stereo display system by the intensity transfer function of every bit in measurement projector.The optical measuring apparatus such as photometer are measured accurately, but can only measure the color of a point at every turn.Obtain projector intensity transfer function a little can only utilize HDR method.The method is measured respectively its brightness output to 255 of each projector brightness inputs.Set respectively a series of time shutter for brightness output each time with digital camera and take pictures, then the image of multiple different exposure time is synthesized to the brightness output of a panel height dynamic image as reduction.Need very many sample image data owing to measuring intensity transfer function, the time of calculating intensity transfer function from image is also very long.About 5 minutes of the computing time of each intensity transfer function in classic method.If measure scalable high resolving power multi-projector free stereo show in the intensity transfer function of every bit in 24 projector, will calculate 24*1024*768 intensity transfer function, computing time is long.Due to the intensity transfer function difference of every bit, gamma correction stage every bit calculates according to different brightness look-up tables.The computing velocity that realizes brightness look-up table in CPU is very slow, and the finite space of video memory makes on GPU, to be difficult to realize the calculating of 1024*768 brightness look-up table simultaneously.

For the speed issue bringing by the intensity transfer function of measurement projector every bit, the present invention sets about improving performance from the following aspects: (1) projection using the projection how much of all projector relevant same visual point image and gamma correction as a virtual projection instrument.The input of this virtual projection instrument is that relevant viewpoint will combine the image of demonstration, and output is the projection on giant-screen after combination shows.By the intensity transfer function of this virtual projection instrument of measurement, this virtual projection instrument is carried out to gamma correction, avoid measurement repeatedly and synthetic calculating of overlapping region.(2) by the measurements and calculations time of B-spline curves and GPU acceleration minimizing intensity transfer function.With the corresponding output on giant-screen of camera measure portion sampling luminance picture input, and pass through GPU Accelerating reduction output brightness by HDR method.Then, calculate the B-spline curves of the input and output point of all sampling brightness of mistake at each location of pixels of virtual projection instrument, thereby obtain continuous intensity transfer function at every bit.(3) in order to make the brightness range after gamma correction as far as possible large, minimum and maximum brightness curved surface is carried out respectively to smoothing processing and obtain the minimum and maximum luminosity response curved surface that vision is consistent, make brightness section after every bit gamma correction between the brightness value of the correspondence position of the consistent minimum and maximum luminosity response curved surface of vision.(4) utilize B-spline function, the GPU that realizes the brightness look-up table that each pixel is different calculates, and is applied in gamma correction.

Projection using the projection after how much of all projector relevant each viewpoint and gamma correction as a virtual projection instrument.The intensity transfer function of measuring every bit in virtual projection instrument carries out gamma correction.The input of this virtual projection instrument is that relevant viewpoint will combine the image of demonstration, and output is the projection on giant-screen after combination shows.Measure the intensity transfer function of virtual projection instrument every bit and carry out the process of gamma correction according to these intensity transfer functions as follows:

(1) server adopts secondary geometric correction method to carry out geometry correction to multi-projector auto-stereo display system.

The first step: the image that shows respectively the unique point composition of equidistant distribution as shown in Figure 2 in each projector frame buffer space.Obtain respectively each projector with digital camera and be projected in the unique point image on screen.The projector space characteristics point of j projector in i viewpoint and the unique point that projects on screen thereof are organized into respectively to projector space initial mesh meshp as shown in Figure 2 _ijthe initial mesh meshd of screen space as shown in Figure 3 _ij.Wherein, i represents the sequence number of viewpoint, i=1, and 2, j represents the sequence number of corresponding described DLP projector in each viewpoint i, j=1,2 ..., 11,12.

Second step: calculate in i viewpoint the correcting area of j projector on screen

dispW _ij=∩(dispA _ij,rect)，i=0,1，j=1,2,…,11,12 （1）

Wherein, dispA _ijbe j projector viewing area on screen in i viewpoint, rect is the region that on screen, combination shows,

$\mathrm{rect}={\&cap;}_{i=1}^{\mathrm{Nv}}\left(\mathrm{inrect}\left({\&cup;}_{j=1}^{\mathrm{Nr}\&times;\mathrm{Nc}}\mathrm{disp}{A}_{\mathrm{ij}}\right)\right)---\left(2\right)$

Mono-of inrect asks the function that connects rectangle in given area.

The 3rd step: at correcting area dispW _ijin regenerate equidistant unique point as shown in Figure 4 and be organized into screen space calibration grid meshnd _ij.According to meshnd _ijeach summit calculate its corresponding projector spatial point.And these projector spatial point are organized into projector free-air correction grid meshnp as shown in Figure 5 _ij.According to meshnd _ijeach summit D(D _u, D _v) calculate its corresponding projector spatial point D ' coordinate (D ' _x, D ' _y) method as follows.

First, be calculated as follows described screen space point D(D _u,, D _v) area coordinate (m, k, w),

$m=\frac{S\left(\mathrm{\&Delta;ABD}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{A}_u& B_u& D_u\\ A_v& B_v& D_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},$ $k=\frac{S\left(\mathrm{\&Delta;DBC}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{D}_u& B_u& C_u\\ D_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},$ $w=\frac{S\left(\mathrm{\&Delta;ADC}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{A}_u& D_u& C_u\\ A_v& D_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_v& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}---\left(3\right)$

Wherein, Δ ABC is that D point is at grid meshd _ijthe triangle (as shown in Figure 6) at middle place, m is the interior triangle Δ ABD of Δ ABC and the ratio of the area of this triangle Δ ABC, k is the interior triangle Δ DBC of Δ ABC and the ratio of the area of this triangle Δ ABC, w is the interior triangle Δ ADC of Δ ABC and the ratio of the area of this triangle Δ ABC, (A _u, A _v), (B _u, B _v) and (C _u, C _v) be three apex coordinates of Δ ABC, (D _u, D _v) be D point coordinate;

Then, be calculated as follows the some D ' in projector space coordinate (D ' _x, D ' _y),

$\left\{\begin{array}{c}{D}_x^{\&prime;}=m\&times;A_x^{\&prime;}+k\&times;B_x^{\&prime;}+w\&times;C_x^{\&prime;}\\ D_y^{\&prime;}=m\&times;A_y^{\&prime;}+k\&times;B_y^{\&prime;}+w\&times;C_y^{\&prime;}\end{array}\right.---\left(4\right)$

Wherein, Δ A ' B ' C ' is at grid meshp _ijin with grid meshd _ijthe corresponding triangle of Δ ABC (as shown in Figure 6), (A ' _x, A ' _y), (B ' _x, B ' _y), (C ' _x, C ' _y) be three apex coordinates of Δ A ' B ' C '.

The 4th step: server dispensed is given the reference position (x of the image of j projector in i viewpoint ^ij _start, y ^ij _start), size (width _ij, height _ij) and distribute to calibration grid meshnp _ijthe texture coordinate (xx on e summit _ije, yy _ije);

$\left\{\begin{array}{c}{x^{\mathrm{ij}}}_{\mathrm{start}}=[({u^{\mathrm{ij}}}_{\min }-u_{\min })/(u_{\max }-u_{\min })]\&times;\mathrm{wd}\\ {y^{\mathrm{ij}}}_{\mathrm{start}}=[({v^{\mathrm{ij}}}_{\min }-v_{\min })/(v_{\max }-v_{\min })]\&times;\mathrm{hd}\end{array}\right.---\left(5\right)$

$\left\{\begin{array}{c}{\mathrm{width}}_{\mathrm{ij}}=[({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })/(u_{\max }-u_{\min })]\&times;\mathrm{wd}\\ {\mathrm{height}}_{\mathrm{ij}}=[{{(v}^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })/(v_{\max }-v_{\min })]\&times;\mathrm{hd}\end{array}\right.---\left(6\right)$

$\left\{\begin{array}{c}{\mathrm{xx}}_{\mathrm{ije}}=(u_{\mathrm{ije}}-{u^{\mathrm{ij}}}_{\min })/({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })\\ {\mathrm{yy}}_{\mathrm{ije}}=(v_{\mathrm{ije}}-{v^{\mathrm{ij}}}_{\min })/({v^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })\end{array}\right.---\left(7\right)$

Wherein, width _ijand height _ijbe image wide and high of distributing to j projector in i viewpoint, wd and hd are wide and high before projection of image of wanting tiled display, (u _min, v _min) and (u _max, v _max) be the apex coordinate that combines the lower left corner and the upper right corner of viewing area rect on giant-screen, u ^ij _min, u ^ij _max, v ^ij _minand v ^ij _maxrespectively correcting area dispW _ijfour apex coordinates in minimum, the maximal value of minimum, maximal value and ordinate of horizontal ordinate, (u _ije, v _ije) be calibration grid meshnp _ijin the coordinate of screen space of giant-screen corresponding to e summit, i=1 ..., Nv, j=1,2 ..., Nr*Nc.

The 5th step: server will combine every piece image of demonstration, intercept corresponding subimage by the reference position calculating, size and distribute to client computer, client computer is mapped to geometry correction grid meshnp by the subimage of distribution by the texture coordinate calculating _ijupper, then export with projector projection, thus the splicing effect of geometric alignment on screen, obtained.

(2) adopt brightness fusion method to carry out Fusion Edges to multi-projector auto-stereo display system.

The first step: the gamma correction template that adopts each projector in brightness calculating fusion multi-projector auto-stereo display system.Be calculated as follows the intensity correction values A that the projector space each point (x, y) of j projector in i viewpoint is located _ij(x, y), is combined into the gamma correction template of this j projector:

$A_{\mathrm{ij}}(x,y)={\left(\frac{a_{\mathrm{ij}}(u,v)}{{\mathrm{\&Sigma;}}_{j^{\&prime;}=1}^{\mathrm{Nr}\&times;\mathrm{Nc}}{a}_{\mathrm{ij}\&prime;}(u,v)}\right)}^{1/\mathrm{\&gamma;}}---\left(8\right)$

Wherein, (u, v) is the screen space coordinates corresponding to projector space (x, y) of j DLP projector of i viewpoint, i=1, and 2, j=1,2 ..., Nr*Nc, γ=2.4, a _ij(u, v) is the correcting area dispW of j projector of i viewpoint _ijmiddle screen space point (u, v) arrives the distance minimum value on its four borders, j '=1, and 2 ..., Nr*Nc, but j ' ≠ j and correcting area dispW _ijwith correcting area dispW _{ij '}there is overlapping region, a _{ij '}(u, v) is the correcting area dispW of i the individual projector of viewpoint j ' _{ij '}middle screen space point (u, v) is to the distance minimum value on its four borders, at Non-overlapping Domain a _{ij '}(u, v)=0.

Second step: reprojection output after the value correspondence of every bit in the image after projector geometry correction and gamma correction template is multiplied each other.Such brightness that obtains projector overlapping region is decayed, and the combination that obtains Fusion Edges shows.

The 3rd step: the projection after all projector relevant each viewpoint are pressed how much of methods and gamma correction is above as the projection of a virtual projection instrument.

(3) calculate the irradiance output of corresponding each sampling brightness input on each location of pixels of each virtual projection instrument.

The first step: get K sampled point by certain interval in the interval [0,255] of brightness value, calculate for the ease of storage below, equilibration time and precision, get K=30, is calculated as follows the brightness value SL of 30 sampled points _k,

${\mathrm{SL}}_k=\left\{\begin{array}{cc}8\&times;(k-1)& 1\&le;k\&le;15\\ 8\&times;(k+2)& 15<k\&le;29\\ 255& k=30\end{array}\right.,k=\mathrm{1,2}...k---\left(9\right)$

Second step: generating size is K the image of xRes X yRes, wherein, xRes=1024, yRes=768.K image I _kin the brightness of every identical, be all k sampling brightness value SL _k, k=1,2 ... K.0.02s get S time shutter Δ t between 2.0s _s, s=1,2 ..., S, wherein, S=16.

The 3rd step: to all images repetitions fourth, fifth and six steps of all virtual projection instrument and second step generation, obtain the irradiance output of corresponding each sampling brightness input in the each pixel in each virtual projection instrument.

The 4th step: show k the image I that second step generates for i virtual projection instrument _kprojection result on screen, it is Δ t that camera is set respectively to the time shutter _s, s=1,2 ..., S, after take pictures, obtaining S size is the image of xcRes X ycRes, wherein, xcRes and ycRes are respectively the wide and high of camera image, xcRes=2288, ycRes=1520.

The 5th step: with setting time shutter Δ t _sthe take pictures brightness value Z of p point in the image obtaining of camera _psirradiance E with this point _pbetween there is following relation,

Z _ps=f(E _pΔt _s)，p=1,2…P （10）

Wherein, f reflects the Nonlinear Mapping relation that the brightness of actual scenery and camera are taken pictures between the brightness of the image that generates, and P is the number of pixels in synthetic image, P=2288 X 1520.If use f ¹represent the inverse function of f,

f ^-1(Z _ps)=E _pΔt _s （11）

Take the logarithm in both sides,

lnf ^-1(Z _ps)=lnE _p+lnΔt _s （12）

Make function g (Z _ps) expression Z _psand E _pwith Δ t _sthe mapping relations of logarithmic function, g=lnf ^-1, so

g(Z _ps)=lnE _p+lnΔt _s （13）

E in above formula _pwith function g the unknown, by solving the least square solution of above formula, the minimum value that namely solves following formula obtains,

$\mathrm{\&Omega;}=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}{\left\{w\left(Z_{\mathrm{ps}}\right)\right[g\left(Z_{\mathrm{ps}}\right)-\ln E_p-\ln \mathrm{\&Delta;}{t}_s\left]\right\}}^2+\mathrm{\&lambda;}\underset{z=Z_{\min }+1}{\overset{Z_{\max }-1}{\mathrm{\&Sigma;}}}{\left[w\left(z\right)g^{\&prime;\&prime;}\left(z\right)\right]}^2---\left(14\right)$

Wherein, w (Z _ps) be to distribute to brightness Z _psweight, λ=50 are smoothing factor, g " be (z) second derivative of g (z),

$w\left(Z_{\mathrm{ps}}\right)=\left\{\begin{array}{cc}{Z}_{\mathrm{ps}}-Z_{\min }& Z_{\mathrm{ps}}\&le;Z_{\mathrm{mid}}\\ Z_{\max }-Z_{\mathrm{ps}}& Z_{\mathrm{ps}}>Z_{\mathrm{mid}}\end{array}\right.---\left(15\right)$

$w\left(z\right)=\left\{\begin{array}{cc}z-Z_{\min }& z\&le;Z_{\mathrm{mid}}\\ Z_{\max }-z& z>Z_{\mathrm{mid}}\end{array}\right.---\left(16\right)$

g″(z)=g(z-1)-2g(z)+g(z+1) （17）

Wherein, Z _minthe brightness minimum value of all pixels in S image, Z _maxthe brightness maximal value of all pixels in S image, Z _mid=(Z _min+ Z _max)/2.

For the robustness of calculating, obtain the irradiance E of p point by the image of multiple time shutter _p,

$\ln E_p=\frac{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(Z_{\mathrm{ps}}\right)(g\left(Z_{\mathrm{ps}}\right)-\ln {\mathrm{\&Delta;t}}_s)}{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(Z_{\mathrm{ps}}\right)},p=\mathrm{1,2}...P---\left(18\right)$

The 6th step: in order to obtain exporting one to one with the input position of described virtual projection instrument at screen space, on corresponding each described irradiance image mapped to grid that each described DLP projector is calculated previous step, and the irradiance image on these grids is superimposed and obtains the output of virtual projection instrument.On grid, the coordinate (x, y) on each summit and texture coordinate (tex_x, tex_y) are respectively

$\left\{\begin{array}{c}x=(D_u-\min x)/(\max x-\min x)*\mathrm{xRes}\\ y=(D_v-\min y)/(\max y-\min y)*\mathrm{yRes}\end{array}\right.---\left(19\right)$

$\left\{\begin{array}{c}\mathrm{tex}\_x=D_u/\mathrm{xcRes}\\ \mathrm{tex}\_y=D_v/\mathrm{ycRes}\end{array}\right.---\left(20\right)$

Wherein, (D _u, D _v) be the screen space coordinates on the summit in the calibration grid of each projector, (minx, and (maxx miny), maxy) be respectively the screen space coordinates in the upper left corner and the lower right corner of whole correcting area, xRes and yRes divide image wide and high that maybe combine demonstration, and xcRes and ycRes are respectively the wide and high of camera image.

(4) in each pixel of virtual projection instrument, obtain the intensity transfer function that B-spline curves represent.

In each pixel of virtual projection instrument, generate K some P _k, k=0,1 ... K-1, wherein, k some P _khorizontal ordinate be k+1, this pixel place sampling brightness value, ordinate is that the irradiance that this pixel place calculates the brightness value input of should sampling is exported.In order to obtain the corresponding relation of continuous input and output brightness, calculate being three Uniform B-spline interpolation curves of this K point, and obtain the reference mark of B-spline curves by following formula,

Wherein, V ₀, V ₁..., V _k+1it is reference mark.Solve the tri-diagonal matrix equation in above formula with chasing method, obtain the reference mark V of three Uniform B-spline interpolation curves ₀, V ₁..., V _k+1.

(5) the consistent minimum and maximum brightness curved surface of computation vision.According to visual theory, the output brightness scope of each point of virtual projection instrument is compressed in different intervals.Calculating can reach the minimum and maximum brightness curved surface that vision is consistent, then the brightness range of each point is compressed to minimum that vision is consistent and high-high brightness curved surface on the interval between the brightness value of this point.So both increased brightness range, the vision of each brightness of the virtual projection instrument output of having got back is consistent.In the consistent minimum brightness curved surface of vision, (u, the brightness value of v) locating is any point

$L^{\&prime;}(u,v)=\max (L\min (u,v),\mathrm{\&lambda;}\&times;\frac{|L\min (u,v)-L\min (u^{\&prime;},v^{\&prime;})|}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(22\right)$

Wherein, Lmin (u, v) the sampling brightness SL minimum for virtual projection instrument shows _mingenerate image time corresponding brightness output image in the brightness at (u, v) coordinate place, (u ', v ') is the neighbor point of (u, v), Lmin (u ', v ') shows minimum sampling brightness SL for virtual projection instrument _mingenerate image time corresponding brightness output image in the brightness at (u ', v ') coordinate place, λ is visually-perceptible coefficient, λ=50, max is the function of maximizing.

In the consistent high-high brightness curved surface of vision, (u, the brightness value of v) locating is any point

$L^{\&prime;\&prime;}(u,v)=\min (L\max (u,v),\mathrm{\&lambda;}\&times;\frac{|L\max (u,v)-L\max (u^{\&prime;},v^{\&prime;})}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(23\right)$

Wherein, Lmax (u, v) the sampling brightness SL maximum for virtual projection instrument shows _maxgenerate image time corresponding brightness output image in the brightness at (u, v) coordinate place, (u ', v ') is the neighbor point of (u, v), Lmax (u ', v ') shows maximum sampling brightness SL for virtual projection instrument _maxgenerate image time corresponding brightness output image in the brightness at (u ', v ') coordinate place.

(6) process of this input brightness on corresponding B-spline curves of the brightness calculation of the image that will show of locating according to virtual projection instrument every bit (x, y) is as follows:

The first step: the reference mark of the B-spline curves of each location of pixels is packaged into respectively to little texture, by synthetic these an all little textures large reference mark texture.In our experiment, each B-spline curves are calculated to 32 reference mark.The horizontal ordinate at each reference mark and ordinate account for respectively a passage in texture.For the 2 d texture of 4 passages, the texture size of 32 reference mark needs is 32*2/4=16.For the ease of the calculating of texture coordinate, the mode that little texture is listed as by 4 row 4 is stored.Large texture is stored each little texture by the mode of the capable xRes row of yRes, wherein, and the resolution that xRes*yRes is display device.So the size of large reference mark texture is (xRes*4) * (yRes*4).

Second step: each location of pixels (x, y) at virtual projection instrument is located, repeats the 3rd step to the six steps below, obtains the brightness input after every bit gamma correction.The brightness value of inputting by change, obtains consistent brightness output.

The 3rd step: the output brightness scope of this point is compressed to minimum that vision is consistent and high-high brightness curved surface on the interval between the brightness value of this point, obtains the brightness output Wl (x, y) that vision is consistent,

Wl(x,y)=Lmin(x,y)+Ol(x,y)/255.0*(Lmax(x,y)-Lmin(x,y))

（24）

Wherein, Ol (x, y) is the image that will the combine demonstration brightness at this point, the sampling brightness SL that Lmin (x, y) is minimum for virtual projection instrument shows _mingenerate image time corresponding brightness output image in the brightness of this point, Lmax (x, y) is that virtual projection instrument shows maximum sampling brightness SL _maxgenerate image time corresponding brightness output image in the brightness of this point.

The 4th step: the reference mark of three Uniform B-Spline Curves of (x, the y) point obtaining according to previous calculations, calculate two end points P of the c section function of three Uniform B-Spline Curves with following formula _cand P (0) _c(1),

$P_c\left(t\right)=\left[\begin{array}{cccc}1& t& t^2& {\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA0000074122970000011.png"\; state="\{\{state\}\}">t</figure-callout>}}^3\end{array}\right]\frac{1}{6}\left[\begin{array}{cccc}1& 4& 1& 0\\ -3& 0& 3& 0\\ 3& -6& 3& 0\\ -1& 3& -3& 1\end{array}\right]\left[\begin{array}{c}{V}_c\\ V_{c+1}\\ V_{c+2}\\ V_{c+3}\end{array}\right],0\&le;t\&le;1,c=\mathrm{0,1},...,K-1---\left(25\right)$

Wherein, the coefficient parameter that t is B-spline curves, c is the call number of function segment, each point between the c section function region that Pc (t) is B-spline curves, Vc, Vc+1, Vc+2, Vc+3 is respectively that the call number of B-spline curves is for being respectively c, c+1, c+2, the reference mark of c+3; According to these end points Pc (0) and Pc (1), find the call number c between function region, make in interval that Wl (x, y) forms at the ordinate value of two end points of c section function.

The 5th step: calculate (x, y) with dichotomy and put the input brightness Nl (x, y) after gamma correction.Be between parametric t original area with [0,1], by getting interval mid point tm, original interval be divided into two.The ordinate E of the point during with formula (25) calculating parameter t=tm on B-spline curves _p.If E _p<Wl (x, y), a half-interval on the Jian Wei left side, new district.If E _p>Wl (x, y) is a half-interval on the right between new district.Constantly interval is divided into two, iteration said process, until interval range is less than the error amount of a setting.Get parametric t for iterating to the interval midrange finally obtaining, calculate the abscissa value of the point on B-spline curves by formula (18), this value is exactly the input brightness Nl (x, y) that Wl (x, y) is corresponding.

The 6th step: Nl (x, y) is multiplied by the gamma correction template obtaining in (2) step, obtains the final brightness input of each projector.The brightness value of inputting by change, obtains consistent brightness output.

Claims (1)

1. the brightness correcting method by pixel response that multi-projector free stereo shows, is characterized in that, contains successively following steps:

Step (1): set up a variable resolution multi-projector auto-stereo display system that there is viewpoint and count two visual point images of I=2, comprise: an array of rear-projectors, an auto-stereoscopic display screen curtain, be called for short screen, a digital camera, a server and multiple client computer below, wherein, array of rear-projectors is made up of 24 DLP projector, each visual point image is pressed the mode tiled display of the capable Nc row of Nr on auto-stereoscopic display screen curtain with Nr × Nc DLP projector, Nr=3, Nc=4; Client computer has 12, two described DLP projector of every client computer control;

Step (2): described server carries out geometry correction to described multi-projector auto-stereo display system, and step is as follows:

Step (2.1): show respectively in the projector space of each projector frame buffer by each client by the image of the unique point composition of the equidistant distribution of setting, form projector space initial mesh meshp _ij, i represents the sequence number of viewpoint, i=1, and 2, j represents the sequence number of corresponding described DLP projector in each viewpoint i, j=1,2 ..., 11,12; Obtain respectively with described digital camera the screen characteristics dot image that the unique point image projection of corresponding each the described DLP projector of each viewpoint forms on described screen again, form the initial mesh meshd of screen space _ij;

Step (2.2): be calculated as follows in i viewpoint the correcting area dispW of j projector on described screen _ij,

dispW _ij=∩(dispA _ij,rect)，i=0,1，j=1,2,…,11,12 （1）

Wherein, dispA _ijbe j projector viewing area on screen in i viewpoint, rect is the region that on described screen, combination shows,

$\mathrm{rect}={\&cap;}_{i=1}^{\mathrm{Nv}}\left(\mathrm{inrect}\left({\&cup;}_{j=1}^{\mathrm{Nr}\&times;\mathrm{Nc}}\mathrm{disp}{A}_{\mathrm{ij}}\right)\right)---\left(2\right)$

In i viewpoint, the summation of totally 12 DLP projector viewing areas on described screen is used

dispA _ijrepresent, mono-of inrect asks the function that connects rectangle in given area;

Step (2.3): j the correcting area dispW that DLP projector shows on described screen in i viewpoint _ijin regenerate by the unique point of described equidistant setting and be organized into described correcting area dispW _ijat the calibration grid meshnd of described screen space _ij; Again according to the calibration grid meshnd of described screen space _ijthe coordinate (D of summit D _u,, D _v) calculate its corresponding projector free-air correction grid meshnp _ijpoint D ' coordinate (D ' _x, D ' _y);

As the calibration grid meshnd of described screen space _ijsummit D(D _u, D _v) area coordinate while being (m, k, w),

$m=\frac{S\left(\mathrm{\&Delta;ABD}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{A}_u& B_u& D_u\\ A_v& B_v& D_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},$ $k=\frac{S\left(\mathrm{\&Delta;DBC}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{D}_u& B_u& C_u\\ D_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_u& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|},$ $w=\frac{S\left(\mathrm{\&Delta;ADC}\right)}{S\left(\mathrm{\&Delta;ABC}\right)}=\frac{\left|\begin{array}{ccc}{A}_u& D_u& C_u\\ A_v& D_v& C_v\\ 1& 1& 1\end{array}\right|}{\left|\begin{array}{ccc}{A}_u& B_v& C_u\\ A_v& B_v& C_v\\ 1& 1& 1\end{array}\right|}---\left(3\right)$

Wherein, Δ ABC is the initial mesh meshd of D point at described screen space _ijthe triangle at middle place, m is the interior triangle Δ ABD of Δ ABC and the ratio of the area of this triangle Δ ABC, k is the interior triangle Δ DBC of Δ ABC and the ratio of the area of this triangle Δ ABC, and w is the interior triangle Δ ADC of Δ ABC and the ratio of the area of this triangle Δ ABC, (A _u, A _v), (B _u, B _v) and (C _u, C _v) be three apex coordinates of Δ ABC;

Described projector free-air correction grid meshnp _ijpoint D ' coordinate (D ' _x, D ' _y) be

$\left\{\begin{array}{c}{D}_x^{\&prime;}=m\&times;A_x^{\&prime;}+k\&times;B_x^{\&prime;}+w\&times;C_x^{\&prime;}\\ D_y^{\&prime;}=m\&times;A_y^{\&prime;}+k\&times;B_y^{\&prime;}+w\&times;C_y^{\&prime;}\end{array}\right.---\left(4\right)$

Wherein, Δ A ' B ' C ' is at described projector space initial mesh meshp _ijin with the initial mesh meshd of described screen space _ijthe corresponding triangle of Δ ABC, three apex coordinates of Δ A ' B ' C ' be respectively (A ' _x, A ' _y), (B ' _x, B ' _y), (C ' _x, C ' _y);

Step (2.4): the calibration grid meshnp that is calculated as follows described server and distributes to by each client j DLP projector in i viewpoint _ijthe reference position (x of image ^ij _start, y ^ij _start), wide high width _ijand height _ij, and distribute to described calibration grid meshnp _ijthe texture coordinate (xx on e summit _ije, yy _ije);

$\left\{\begin{array}{c}{x^{\mathrm{ij}}}_{\mathrm{start}}=[({u^{\mathrm{ij}}}_{\min }-u_{\min })/(u_{\max }-u_{\min })]\&times;\mathrm{wd}\\ {y^{\mathrm{ij}}}_{\mathrm{start}}=[({v^{\mathrm{ij}}}_{\min }-v_{\min })/(v_{\max }-v_{\min })]\&times;\mathrm{hd}\end{array}\right.---\left(5\right)$

$\left\{\begin{array}{c}{\mathrm{width}}_{\mathrm{ij}}=[({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })/(u_{\max }-u_{\min })]\&times;\mathrm{wd}\\ {\mathrm{height}}_{\mathrm{ij}}=[{{(v}^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })/(v_{\max }-v_{\min })]\&times;\mathrm{hd}\end{array}\right.---\left(6\right)$

$\left\{\begin{array}{c}{\mathrm{xx}}_{\mathrm{ije}}=(u_{\mathrm{ije}}-{u^{\mathrm{ij}}}_{\min })/({u^{\mathrm{ij}}}_{\max }-{u^{\mathrm{ij}}}_{\min })\\ {\mathrm{yy}}_{\mathrm{ije}}=(v_{\mathrm{ije}}-{v^{\mathrm{ij}}}_{\min })/({v^{\mathrm{ij}}}_{\max }-{v^{\mathrm{ij}}}_{\min })\end{array}\right.---\left(7\right)$

Wherein, width _ijand height _ijthe calibration grid meshnp of described server-assignment to j DLP projector in i viewpoint _ijimage wide and high, wd and hd are wide and high before projection of image of wanting tiled display on described screen, (u _min, v _min) and (u _max, v _max) be the apex coordinate that combines the lower left corner and the upper right corner of viewing area rect on described screen, u ^ij _min, u ^ij _max, v ^ij _minand v ^ij _maxrespectively correcting area dispW _ijfour apex coordinates in minimum, the maximal value of minimum, maximal value and ordinate of horizontal ordinate, (u _ije, v _ije) be calibration grid meshnp _ijin the coordinate of screen space of screen corresponding to e summit, i=1,2, j=1,2 ..., Nr*Nc;

Step (2.5): server will combine each client in program every piece image of demonstration, the reference position, the size that calculate by step (2.4) intercept corresponding subimage and distribute to corresponding client computer, to the subimage of distribution is mapped to corresponding geometry correction grid meshnp by the described texture coordinate calculating _ijupper, then export with projector projection, the splicing effect of geometric alignment on described screen, obtained;

Step (3): adopt according to the following steps successively brightness fusion method to carry out transkit attenuation to the brightness at the edge of each DLP projector overlapping region on screen described in described multi-projector auto-stereo display system;

Step (3.1): be calculated as follows the intensity correction values A that the projector space each point (x, y) of j projector in i viewpoint is located _ij(x, y), is combined into the gamma correction template of this j projector:

$A_{\mathrm{ij}}(x,y)={\left(\frac{a_{\mathrm{ij}}(u,v)}{{\mathrm{\&Sigma;}}_{j^{\&prime;}=1}^{\mathrm{Nr}\&times;\mathrm{Nc}}{a}_{\mathrm{ij}\&prime;}(u,v)}\right)}^{1/\mathrm{\&gamma;}}---\left(8\right)$

Wherein, (u, v) is the screen space coordinates corresponding to projector space (x, y) of j DLP projector of i viewpoint, i=1, and 2, j=1,2 ..., Nr*Nc, γ=2.4, a _ij(u, v) is the correcting area dispW of j projector of i viewpoint _ijmiddle screen space point (u, v) arrives the distance minimum value on its four borders, j '=1, and 2 ..., Nr*Nc, but j ' ≠ j and correcting area dispW _ijwith correcting area dispW _{ij '}there is overlapping region, a _{ij '}(u, v) is the correcting area dispW of i the individual projector of viewpoint j ' _{ij '}middle screen space point (u, v) is to the distance minimum value on its four borders, at Non-overlapping Domain a _{ij '}(u, v)=0;

Step (3.2): reprojection output after the value correspondence of every bit in the value of the every bit of image after projector geometry correction and gamma correction template is multiplied each other, thus the combination that obtains the brightness decay of projector overlapping region shows;

Step (3.3): all DLP projector relevant each viewpoint are carried out to projector image after geometry and the gamma correction projected image as a virtual projection instrument by step (1) and step (2);

Step (4): the irradiance value of calculating according to the following steps successively corresponding each sampling brightness input on each location of pixels of each described virtual projection instrument;

Step (4.1): get K sampled point by certain interval in the interval [0,255] of brightness value, calculate for the ease of storage below, equilibration time and precision, get K=30, is calculated as follows the brightness value SL of 30 sampled points _k,

${\mathrm{SL}}_k=\left\{\begin{array}{cc}8\&times;(k-1)& 1\&le;k\&le;15\\ 8\&times;(k+2)& 15<k\&le;29\\ 255& k=30\end{array}\right.,k=\mathrm{1,2}...k---\left(9\right)$

Step (4.2): generating size is K the image of xRes X yRes, xRes and yRes divide image wide and high that maybe combine demonstration, wherein, K=30, xRes=1024, yRes=768; K image I _kin the brightness of every identical, be all k sampling brightness value SL _k, k=1,2 ... K; 0.02s get S time shutter Δ t between 2.0s _s, s=1,2 ..., S, wherein S=16;

Step (4.3): all images to all virtual projection instrument and step (4.2) generation repeat following step (4.3.1)～step (4.3.2), obtain the irradiance value of corresponding each sampling brightness input in the each pixel in each virtual projection instrument;

Step (4.3.1): k the image I generating for i the virtual projection instrument step display (4.2) described in step (3.3) _kprojection result on screen is Δ t camera being set respectively to the time shutter _s, s=1,2 ..., S, after take pictures, obtaining the individual size of S ' is the image of xcRes X ycRes, wherein, S '=S, xcRes and ycRes are respectively camera image wide and high after exposure is taken pictures, xcRes=2288, ycRes=1520;

Step (4.3.2): with setting time shutter Δ t _sthe take pictures brightness value Z of p point in the described image of obtaining step (4.3.1) of camera _psirradiance E with this point _p,

$\ln E_p=\frac{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(Z_{\mathrm{ps}}\right)(g\left(Z_{\mathrm{ps}}\right)-\ln {\mathrm{\&Delta;t}}_s)}{{\mathrm{\&Sigma;}}_{s=1}^{S}w\left(Z_{\mathrm{ps}}\right)},p=\mathrm{1,2}...P---\left(10\right)$

Wherein, P is the number of pixels in each image, P=2288*1520, function g (Z _ps) be Z _psand E _pwith Δ t _sthe mapping relations of logarithmic function,

g(Z _ps)=lnE _p+lnΔt _s （11）

W (Z _ps) be to distribute to brightness Z _psweight,

$w\left(Z_{\mathrm{ps}}\right)=\left\{\begin{array}{cc}{Z}_{\mathrm{ps}}-Z_{\min }& Z_{\mathrm{ps}}\&le;Z_{\mathrm{mid}}\\ Z_{\max }-Z_{\mathrm{ps}}& Z_{\mathrm{ps}}>Z_{\mathrm{mid}}\end{array}\right.---\left(12\right)$

Wherein, Z _minthe brightness minimum value of all pixels in S image, Z _maxthe brightness maximal value of all pixels in S image, Z _mid=(Z _min+ Z _max)/2;

Step (4.3.3): in order to obtain exporting one to one with the input position of described virtual projection instrument at screen space, on corresponding each described irradiance image mapped to grid that each described DLP projector is calculated step (4.3.2), and the irradiance image on these grids is superimposed and obtains the output of virtual projection instrument; On grid, the coordinate (x, y) on each summit and texture coordinate (tex_x, tex_y) are respectively

$\left\{\begin{array}{c}x=(D_u-\min x)/(\max x-\min x)*\mathrm{xRes}\\ y=(D_v-\min y)/(\max y-\min y)*\mathrm{yRes}\end{array}\right.---\left(13\right)$

$\left\{\begin{array}{c}\mathrm{tex}\_x=D_u/\mathrm{xcRes}\\ \mathrm{tex}\_y=D_v/\mathrm{ycRes}\end{array}\right.---\left(14\right)$

Wherein, (D _u, D _v) be summit in the calibration grid of the each projector coordinate at screen space, (minx, and (maxx miny), maxy) be respectively the upper left corner of whole correcting area and the lower right corner coordinate at screen space, xRes and yRes divide image wide and high that maybe combine demonstration, and xcRes and ycRes are respectively the wide and high of camera image;

Step (5): generate K some P in each pixel of virtual projection instrument _k, k=0,1 ... K-1, K=30, wherein, k some P _khorizontal ordinate be k+1, this pixel place sampling brightness value, ordinate is the irradiance value that this pixel place calculates the brightness value input of should sampling; In order to obtain the corresponding relation of continuous input and output brightness, calculate being three Uniform B-spline interpolation curves of this K point, and obtain the reference mark of B-spline curves by following formula,

Wherein, V ₀, V ₁..., V _k+1it is reference mark; Solve the tri-diagonal matrix equation in above formula with chasing method, obtain the reference mark V of three Uniform B-spline interpolation curves ₀, V ₁..., V _k+1;

Step (6): in the minimum brightness curved surface that in calculating screen space, vision is consistent, (u, the brightness value of v) locating is any point

$L^{\&prime;}(u,v)=\max (L\min (u,v),\mathrm{\&lambda;}\&times;\frac{|L\min (u,v)-L\min (u^{\&prime;},v^{\&prime;})|}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(16\right)$

Wherein, Lmin (u, v) the sampling brightness SL minimum for virtual projection instrument shows _mingenerate image time corresponding brightness output image in the brightness at (u, v) coordinate place, (u ', v ') is the neighbor point of (u, v), Lmin (u ', v ') shows minimum sampling brightness SL for virtual projection instrument _mingenerate image time corresponding brightness output image in the brightness at (u ', v ') coordinate place, λ is visually-perceptible coefficient, λ=50, max is the function of maximizing;

In the high-high brightness curved surface that in calculating screen space, vision is consistent, (u, the brightness value of v) locating is any point

$L^{\&prime;\&prime;}(u,v)=\min (L\max (u,v),\mathrm{\&lambda;}\&times;\frac{|L\max (u,v)-L\max (u^{\&prime;},v^{\&prime;})}{\sqrt{{|u-u^{\&prime;}|}^2+{|v-v^{\&prime;}|}^2}})---\left(17\right)$

Wherein, Lmax (u, v) the sampling brightness SL maximum for virtual projection instrument shows _maxgenerate image time corresponding brightness output image in the brightness at (u, v) coordinate place, (u ', v ') is the neighbor point of (u, v), Lmax (u ', v ') shows maximum sampling brightness SL for virtual projection instrument _maxgenerate image time corresponding brightness output image in the brightness at (u ', v ') coordinate place;

Step (7): the process of this input brightness on corresponding B-spline curves of the brightness calculation of the image that will show of locating according to virtual projection instrument every bit (x, y) according to the following steps is successively as follows:

Step (7.1): the reference mark of the B-spline curves of each location of pixels is packaged into respectively to little texture, by synthetic these an all little textures large reference mark texture; Each B-spline curves are calculated to 32 reference mark; The horizontal ordinate at each reference mark and ordinate account for respectively a passage in texture; For the 2 d texture of 4 passages, the texture size of 32 reference mark needs is 32*2/4=16; For the ease of the calculating of texture coordinate, the mode that little texture is listed as by 4 row 4 is stored; Large texture is capable by described yRes, the mode of xRes row is stored each little texture, wherein, and the resolution that xRes*yRes is display device; So the size of large reference mark texture is (xRes*4) * (yRes*4);

Step (7.2): each location of pixels (x, y) at virtual projection instrument is located, repeats step (7.2.1)～step (7.2.4) below, obtains the brightness input after every bit gamma correction; The brightness value of inputting by change, obtains consistent brightness output;

Step (7.2.1): the output brightness scope of this point is compressed to minimum that vision is consistent and high-high brightness curved surface on the interval between the brightness value of this point, obtains the brightness output Wl (x, y) that vision is consistent,

Wl(x,y)=Lmin(x,y)+Ol(x,y)/255.0*(Lmax(x,y)-Lmin(x,y)) （18）

Wherein, Ol (x, y) is the image that will the combine demonstration brightness at this point, the sampling brightness SL that Lmin (x, y) is minimum for virtual projection instrument shows _mingenerate image time corresponding brightness output image in the brightness of this point, Lmax (x, y) is that virtual projection instrument shows maximum sampling brightness SL _maxgenerate image time corresponding brightness output image in the brightness of this point;

Step (7.2.2): the reference mark of three Uniform B-Spline Curves of (x, the y) point obtaining according to previous calculations, calculate two end points P of the c section function of three Uniform B-Spline Curves with following formula _cand P (0) _c(1),

$P_c\left(t\right)=\left[\begin{array}{cccc}1& t& t^2& t^3\end{array}\right]\frac{1}{6}\left[\begin{array}{cccc}1& 4& 1& 0\\ -3& 0& 3& 0\\ 3& -6& 3& 0\\ -1& 3& -3& 1\end{array}\right]\left[\begin{array}{c}{V}_c\\ V_{c+1}\\ V_{c+2}\\ V_{c+3}\end{array}\right],0\&le;t\&le;1,c=\mathrm{0,1},...,K-1---\left(19\right)$

Wherein, the coefficient parameter that t is B-spline curves, c is the call number of function segment, P _c(t) be each point between the c section function region of B-spline curves, V _c, V _c+1, V _c+2, V _c+3be respectively the call number of B-spline curves for being respectively c, c+1, c+2, the reference mark of c+3; According to these end points P _cand P (0) _c(1), find the call number c between function region, make in interval that Wl (x, y) forms at the ordinate value of two end points of c section function;

Step (7.2.3): calculate (x, y) with dichotomy and put the input brightness Nl (x, y) after gamma correction: be between parametric t original area with [0,1], by getting interval mid point tm, original interval be divided into two; The ordinate E of the point during with formula (19) calculating parameter t=tm on B-spline curves _p; If Ep<Wl (x, y), a half-interval on the Jian Wei left side, new district; If Ep>Wl (x, y) is a half-interval on the right between new district; Constantly interval is divided into two, iteration said process, until interval range is less than the error amount of a setting; Get parametric t for iterating to the interval midrange finally obtaining, calculate the abscissa value of the point on B-spline curves by formula (18), this abscissa value is exactly the input brightness Nl (x, y) that Wl (x, y) is corresponding;

Step (7.2.4): Nl (x, y) is multiplied by the gamma correction template obtaining in step (3), obtains the final brightness input of each projector; The brightness value of inputting by change, obtains consistent brightness output.

Images