CN114359583A - Gradient histogram angle rapid calculation method - Google Patents
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Abstract
The invention adopts a simple and convenient way to conveniently and rapidly calculate the gradient direction, and particularly provides a method for rapidly calculating the gradient histogram angle, which comprises the following steps: s1, if the direction of the image is defined as the included angle a between gx and gy, the original gradient direction calculation method is: a ═ arctan (gy/gx), i.e.: tan a ═ gy/gx, where gx and gy are the gradients of the image at the (x, y) point in the x-direction and y-direction, respectively; s2, assuming that N directions are divided from 0 ° to 180 °, not divided into positive and negative, and an unsigned gradient, each N degree is a direction where [0 ° - (N/2) ° ], ((180-N/2) ° -180 ° ] is ori _1, where N is a positive integer greater than 1, the angle N of each direction is 180/N, S3, since the tan value of each boundary angle is known, it is directly determined by the correspondence that the direction ori is the several direction from the 1 st direction to the N th direction from the value of tan a, dy/dx.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a method for rapidly calculating an angle of a gradient histogram.
Background
In the prior art, the method of calculating the image gradient is generally performed as follows:
1. calculating the gradient direction and amplitude of the image
For image pixel point (i, j): the gradient Hx (i, j) of the X-direction and the gradient Hy (i, j) of the Y-direction
Hx(i,j)＝I(i+1,j)-I(i,j)
Hy(i,j)＝I(i,j)-I(i,j+1)
The image can be convolved using the gradient operator sobel, Laplacian.
The gradient amplitude M (x, y) and the gradient direction θ (x, y) can thus be determined:
θ(x,y)＝arctan(Hy/Hx)
2. calculating bin value
The gradient direction θ is [0,180], which is divided into n bins. For example, in OpenCV, n is 9, i.e., a circle is divided into 9 parts, each part interval corresponds to a bin value, e.g., 0 ≦ θ <40 corresponds to a bin 0, and when a certain gradient direction is in the range of [0,40), it corresponds to a bin 0 plus 1, and the magnitude is the weight when calculating the number of bins, and then in the above example, if M is 2, then a bin 0 plus 1 is 2. This results in a count for each bin.
The angles are 0-180 degrees and not 0-360 degrees, this is called "unsigned" gradients because a gradient and its negative are represented by the same number, i.e., the arrow of a gradient and the direction of the arrow after it has been rotated 180 degrees are considered the same, and it has been found in experiments that unsigned gradients perform better than signed gradients (0-360 degrees) in human target detection tasks.
3. Counting bin numbers to form HOG descriptor
The statistics are performed in a window area of an image, and the area size and the sliding mode are determined using parameters such as cellSize, blockSize, blockStride, and winSize.
In each Cell, gradient direction statistics is independently performed, so that a histogram with the gradient direction as a horizontal axis shows that the gradient direction can be 0-180 degrees or 0-360 degrees, but the dalal experiment shows that a better result can be obtained for detecting the direction range of 0-180 degrees, namely the direction range with a positive or negative neglected degree. This gradient profile is then divided equally into 9 orientation bins, each of which corresponds to a square column, as shown in FIG. 2.
The image gradient direction is involved in calculating the HOG feature of the image, arctan is needed to calculate the gradient direction value in practical programming from the viewpoint of the gradient direction definition of the image, and the step is in a large cycle, so that the calculation is slow and complex.
Furthermore, technical terms commonly used in the art include:
histogram of organized grids, abbreviated as HOG, is a feature commonly used in the field of computer vision and pattern recognition to describe local textures of images. It constructs features by calculating and counting the histogram of gradient direction of local area of image. The common method is that Hog characteristics are combined with SVM to carry out image recognition and classification.
2. Image gradient values and directions:
in calculus, the basic definition of the first order differential of a one-dimensional function is such that:
df/dx＝lim(f(x+∈)-f(x))/∈(∈→0)。
disclosure of Invention
In order to solve the problems in the prior art, the present invention aims to: the gradient direction is conveniently and rapidly calculated in a simple and convenient mode.
Specifically, the invention provides a method for rapidly calculating an angle of a gradient histogram, which comprises the following steps:
s1, if the direction of the image is defined as the included angle a between gx and gy, the original gradient direction calculation method is:
a ═ arctan (gy/gx), i.e.: tan a ═ gy/gx, where gx and gy are the gradients of the image at the (x, y) point in the x-direction and y-direction, respectively;
s2, assuming that N directions are divided by 0 ° to 180 °, plus and minus, unsigned gradients, one direction per N degrees, where [0 ° — (N/2) ° ], ((180-N/2) ° -180 ° ] is ori _1, where N is a positive integer greater than 1, the angle N for each direction is 180/N, i.e.:
at S3, since the tan value of each boundary angle is known, it is directly determined from the tan a, that is, the value of dy/dx that the direction ori is the several direction from the 1 st direction to the nth direction by the correspondence relationship.
In the method, the degree from zero to 180 degrees is divided into N directions, N is determined according to the actual situation, the calculation mode is unchanged, and the tan value is correspondingly changed according to the actual division.
The step S2 further includes: let N be 9 directions, not divided into positive and negative, unsigned gradient, and each N be 20 degrees, which is one direction, where 0 ° -10 °, 170 ° -180 ° is ori _1, that is:
| angle A | Direction ori |
| (0°,10°),(170°,180°) | ori＝1 |
| (10°,30°) | ori＝2 |
| (30°,50°) | ori＝3 |
| (50°,70°) | ori＝4 |
| (70°,90°) | ori＝5 |
| (90°,110°) | ori＝6 |
| (110°,130°) | ori＝7 |
| (130°,150°) | ori＝8 |
| (150°,170°) | ori＝9 |
。
In step S3, it is directly determined from the relation of correspondence that the direction ori is the fifth direction by dy/dx, that is:
| tanA | direction ori |
| dx＝0 | ori＝5 |
| (-0.1763,0.1763) | ori＝1 |
| (0.1763,0.5774) | ori＝2 |
| (0.5774,1.1918) | ori＝3 |
| (1.1918,2.7475) | ori＝4 |
| (2.7475,) | ori＝5 |
| (,-2.7475) | ori＝6 |
| (-2.7475,-1.1918) | ori＝7 |
| (-1.1918,-0.5774) | ori＝8 |
| (-0.5774,-0.1763) | ori＝9 |
。
Here, ori is 5, which is actually calculated, and when dx is 0, dy/dx- > ∞, arctan (∞) — 90, that is, the corresponding angle is 90 degrees, so ori is 5.
(2.7475,) denotes > 2.7475;
(, -2.7475) represents < -2.7475;
in the method, the image is a two-dimensional function f (x, y), and the differential is a partial differential; therefore, there are:
because the image is a discrete two-dimensional function, the epsilon cannot be infinitely small, the image is discrete according to pixels, and the minimum epsilon is 1 pixel; the above image differentiation therefore becomes again of the form in which e is 1:
these are the gradients of the image in the x-direction and y-direction, respectively, at the (x, y) point, which, as seen from the above expression, corresponds to the difference between 2 adjacent pixels.
The gradients in the x-direction and the y-direction may be represented together by the following equation:
the operation of approximating the square and square root with absolute values reduces the amount of computation:
M(x,y)＝|gx|+|gy|。
the method can further convert the division operation comparison of dy/dx into multiplication operation comparison or into integer calculation on the basis of the multiplication operation comparison.
In summary, the method of the present application can achieve the following advantages: the image gradient direction is involved in the calculation of the HOG characteristics of the image, and the calculation speed can be increased and the calculation steps can be simplified by using the method in the actual programming from the definition of the image gradient direction.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention.
FIG. 1 is a schematic block flow diagram of the method of the present invention.
Fig. 2 is a schematic diagram of a histogram with gradient direction as horizontal axis involved in the method of the present invention.
FIG. 3 is a schematic diagram of the method of the present invention in which the gradient direction is divided into 9 directions, wherein the gradient is not divided into positive and negative, but is unsigned.
Detailed Description
In order that the technical contents and advantages of the present invention can be more clearly understood, the present invention will now be described in further detail with reference to the accompanying drawings.
In calculating the image gradient values and directions: in calculus, if the image is a two-dimensional function f (x, y), the derivative is, of course, partial. Therefore, there are:
because the image is a discrete two-dimensional function, e cannot be infinitely small, the image is discrete by pixel, and the smallest e is 1 pixel. The above image differentiation therefore becomes again of the form (∈ ═ 1):
these are the gradients of the image in the x-direction and y-direction, respectively, at the (x, y) point, which, as can be seen from the above expression, corresponds to the difference between 2 adjacent pixels.
The gradients in the x and y directions can be represented together by the following equation:
here, the square is also the square, and the square is also the open, the calculation amount is relatively large, so the operation of approximating the square and the square root by the absolute value is generally used to reduce the calculation amount:
M(x,y)＝|gx|+|gy|
the direction of the image is defined as the angle A between gx and gy
tanA＝gy/gx
The following can be obtained:
A＝arctan(gy/gx)。
therefore, as shown in fig. 1, the present application relates to a method for fast calculating gradient histogram angle, comprising the following steps:
s1, if the direction of the image is defined as the included angle a between gx and gy, the original gradient direction calculation method is:
a ═ arctan (gy/gx), i.e.: tan a ═ gy/gx, where gx and gy are the gradients of the image at the (x, y) point in the x-direction and y-direction, respectively;
s2, assuming that N directions are divided by 0 ° to 180 °, plus and minus, unsigned gradients, one direction per N degrees, where [0 ° — (N/2) ° ], ((180-N/2) ° -180 ° ] is ori _1, where N is a positive integer greater than 1, the angle N for each direction is 180/N, i.e.:
at S3, since the tan value of each boundary angle is known, it is directly determined from the tan a, that is, the value of dy/dx that the direction ori is the several direction from the 1 st direction to the nth direction by the correspondence relationship.
Specifically, the following is further described:
original gradient direction calculation mode:
A＝arctan(dy/dx)
namely:
tanA＝dy/dx
it is assumed that there are 9 directions (not positive and negative, unsigned gradients) as shown in fig. 3.
Every 20 degrees is a direction, specifically 0-10, 170-180 is ori _1, i.e.:
A～(0°,10°),(170°,180°):ori＝1
A～(10°,30°):ori＝2
A～(30°,50°):ori＝3
A～(50°,70°):ori＝4
A～(70°,90°):ori＝5
A～(90°,110°):ori＝6
A～(110°,130°):ori＝7
A～(130°,150°):ori＝8
A～(150°,170°):ori＝9
however, the tan value of each boundary angle is known, so that ori can be directly determined as the direction from tanA, dy/dx, that is:
dx＝0:ori＝5
dy/dx～(-0.1763,0.1763):ori＝1
dy/dx～(0.1763,0.5774):ori＝2
dy/dx～(0.5774,1.1918):ori＝3
dy/dx～(1.1918,2.7475):ori＝4
dy/dx～(2.7475,):ori＝5
dy/dx～(,-2.7475):ori＝6
dy/dx～(-2.7475,-1.1918):ori＝7
dy/dx～(-1.1918,-0.5774):ori＝8
dy/dx～(-0.5774,-0.1763):ori＝9
in actual programming, the division comparison of dy/dx can be further converted into multiplication comparison, or converted into integer calculation on the basis, so that the operation efficiency is further improved.
In addition, it is explicitly stated in the present application that 180 degrees is divided into N directions, so that the user can determine N according to actual conditions, the above calculation method is not changed, and the tan value may vary according to actual division.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the embodiment of the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. A method for fast computing gradient histogram angles is characterized by comprising the following steps:
s1, if the direction of the image is defined as the included angle a between gx and gy, the original gradient direction calculation method is:
a ═ arctan (gy/gx), i.e.: tan a ═ gy/gx, where gx and gy are the gradients of the image at the (x, y) point in the x-direction and y-direction, respectively;
s2, assuming that N directions are divided by 0 ° to 180 °, plus and minus, unsigned gradients, one direction per N degrees, where [0 ° — (N/2) ° ], ((180-N/2) ° -180 ° ] is ori _1, where N is a positive integer greater than 1, the angle per direction is N180/N, i.e.:
at S3, since the tan value of each boundary angle is known, it is directly determined from the tan a, that is, the value of dy/dx that the direction ori is the several direction from the 1 st direction to the nth direction by the correspondence relationship.
2. The method as claimed in claim 1, wherein the method divides the degree from zero to 180 degrees into N directions, determines N according to the actual situation, the calculation is not changed, and the tan value varies according to the actual division.
3. The method for fast computing gradient histogram angle according to claim 1, wherein the step S2 further comprises: let N be 9 directions, not divided into positive and negative, unsigned gradient, and each N be 20 degrees, which is one direction, where 0 ° -10 °, 170 ° -180 ° is ori _1, that is:
。
4. The method as claimed in claim 3, wherein the step S3 directly determines that the direction ori is the fifth direction from tan A, dy/dx according to the corresponding relationship, that is:
5. a method for fast computation of gradient histogram angles according to claim 3, characterized in that in said method the image is a two-dimensional function f (x, y) whose differential is of course partial differential; therefore, there are:
because the image is a discrete two-dimensional function, the epsilon cannot be infinitely small, the image is discrete according to pixels, and the minimum epsilon is 1 pixel; the above image differentiation therefore becomes again of the form in which e is 1:
these are the gradients of the image in the x-direction and y-direction, respectively, at the (x, y) point, which, as seen from the above expression, corresponds to the difference between 2 adjacent pixels.
6. A method for fast computation of gradient histogram angles as claimed in claim 5, wherein the gradients in x-direction and y-direction are represented together by the following sub-equations:
the operation of approximating the square and square root with absolute values reduces the amount of computation:
M(x,y)＝|gx|+|gy|。
7. the method as claimed in claim 1, wherein the method further converts dy/dx division comparison into multiplication comparison, or further converts the division comparison into integer calculation based on the multiplication comparison.
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