CN102033933A - Distance metric optimization method for maximizing mean average precision (MAP) - Google Patents

Abstract

The invention discloses a distance measurement optimization method for maximizing the average precision rate (MAP), which comprises the following steps: (1) obtaining an image database containing a query image-to-be-queried image pair set; (2) using a smoothing function to MAP performs approximation, converts it into an objective function and adds a regularization term, so that the objective function is continuously differentiable; (3) Using the query image-to-be-queried image pair in the image database, the optimization technique based on gradient descent is used to optimize the The function is optimized, and the optimization process is repeated, and the solution that maximizes the MAP is taken as the optimal linear transformation matrix; (4) The distance measure defined by the optimal linear transformation matrix is obtained. This method has the characteristics of optimization process and direct target, and the distance measure obtained by this method can achieve better image retrieval performance.

Description

Optimal distance measure method for maximizing the mean of average precision

technical field

The invention relates to a distance measure optimization method for improving image retrieval performance, in particular to a distance measure optimization method for maximizing the mean value of the average precision rate.

Background technique

The basic idea of content-based image retrieval (Content-Based Image Retrieval, CBIR) is to extract the visual features of the image, and use the visual features as an index to achieve higher-level image retrieval. CBIR technology can provide support and assistance for image data management, clinical diagnosis, medical teaching, etc. In particular, the retrieval of similar lesions in medical images can improve the reliability of clinical diagnosis and the integrity of relevant information.

Generally, in order to allow the query results to be returned in descending order of similarity, the CBIR system needs to define a distance measure or similarity measure in the image feature space to measure the difference between the image to be queried and the query image in the database, and return In the result, the images to be queried are sorted according to the difference. Commonly used distance measures are: Euclidean distance, Mahalanobis distance, Cauchy distance, etc. The retrieval performance of a CBIR system largely depends on two aspects: 1. Visual features used to express image content and semantic concepts; 2. Distance measure or similarity measure defined in the feature space. CBIR systems usually use low-level visual features, such as color, texture, shape, edge, etc., to describe image content. However, low-level visual features have limited ability to describe, and information will be lost when expressing images, so low-level visual features generally cannot directly express or reflect the high-level semantics of images. In this way, in the low-level feature space, it is difficult for us to use the above-mentioned general distance measure to define a similarity measure closely related to semantic concepts, that is, there is a so-called "semantic gap", which makes the retrieval performance of the CBIR system far from the actual demand. .

Relevance Feedback and Distance Metric Learning methods can be used to reduce the semantic gap and improve the retrieval performance of CBIR. The data used for learning in relational feedback is difficult to obtain, and the system needs multiple adjustments to achieve satisfactory results, which is not very convenient for users to use. The distance measure learning method can establish a mapping between low-level image features and high-level semantics based on pre-labeled image samples, thereby defining a distance measure that reflects semantic differences and improving retrieval performance. The existing distance measure learning methods are mostly designed for clustering or k-nearest neighbor classification problems, and the learning goal is to improve the accuracy of clustering or k-nearest neighbor classification. However, the retrieval accuracy index of the CBIR system is very different from the classification accuracy rate, such as Mean Average Precision (MAP) and NDCG (Normalized Discounted Cumulative Gain), which are related to the ordering of the images to be queried in the database , using optimized objective functions designed for clustering or classification problems for distance measure learning may not necessarily obtain the best distance measure for retrieval performance. Moreover, since the retrieval accuracy index is not continuously differentiable, it is difficult to optimize it.

Contents of the invention

The object of the present invention is to provide a distance measure optimization method for maximizing the mean value of the average precision rate. This method has an optimization process and a direct target. The distance measure obtained by optimization can reflect the semantic difference of the image. The distance measure obtained by the method can be achieve better image retrieval performance.

The purpose of the present invention can be achieved through the following technical measures:

A distance measure optimization method for maximizing the average precision rate, comprising the following steps:

(1) Obtain an image database that includes a collection of query image-image pairs to be queried;

(2) Approximating MAP with a smooth function, converting it into an objective function and adding a regularization term, so that the objective function is continuously differentiable;

(3) Using the query image-to-be-queried image pair in the image database, the objective function is optimized using a method based on gradient descent, and the optimization process is repeated, and the solution that maximizes the MAP is taken as the optimal linear transformation matrix;

(4) Acquisition of the distance measure between images, including two ways: use the optimal linear transformation matrix in step (3) to transform the image features in the image database first, and then use the Euclidean distance of the transformed features to define the distance between images distance measure; or use the optimal linear transformation matrix in step (3) to define the Mahalanobis distance as the distance measure between images.

The image database in the step (1) is composed of images or image region features and image categories.

In the step (1), it is determined whether the image pair is related according to whether it contains the same anatomical structure, the same type of lesion, etc., and the query-to-be-queried image pair is marked.

The process of approximating the MAP in the step (2) is: for a given query image, the sequence number of any image to be queried is smoothly approximated using a Sigmoid function, and then the smooth approximation of the MAP is obtained.

The sequence number of the image to be queried is determined by comparing the distance between the image to be queried and all other images to be queried and the query image.

The initial solution of the transformation matrix in the step (3) can be a random matrix or a transformation matrix obtained by other methods.

In the step (3), a stochastic gradient descent algorithm is used to optimize the objective function.

Compared with the prior art, the inventive method has the following beneficial effects:

1. This method involves technologies such as image retrieval, statistical learning, and numerical optimization. Through statistical learning, the Mean Average Precision (MAP) is directly optimized, which can be used for image retrieval, cluster analysis, data reduction, etc. This method mainly performs statistical learning on the labeled image data, obtains a linear transformation matrix, maps the original feature space to a new more discriminative feature space, and uses Euclidean distance as the image similarity measure in the new feature space Search to achieve a higher MAP.

2. The method of the present invention directly solves the linear transformation matrix without using the time-consuming semi-positive definite programming algorithm to solve it, and can directly adjust the dimension of the transformation matrix to perform dimension reduction on the original features instead of performing the rank reduction on the semi-positive definite matrix. Constrained or indirectly adjusted regularization parameters to achieve dimensionality reduction. This method takes the smooth approximation of the retrieval accuracy index MAP as the objective function. Compared with some other distance measure learning methods, the optimization process and objectives are more direct. The mapped low-level image features are more closely related to the high-level semantic features, and the retrieval performance is better. . In content-based medical image retrieval applications, the invention can achieve better retrieval performance than distance measures obtained by other distance measure learning methods.

3. Since the calculation of the objective function and gradient for all query images-to-be-queried images is very large, therefore, this method adopts the stochastic gradient descent algorithm for optimization, which can reduce the demand for computer memory and speed up the convergence of the algorithm; In addition, since the objective function is non-convex, there are many local extremum points in the solution space. In order to prevent the solution from falling into local extremum points, an initial solution closer to the optimal solution is estimated by other faster distance measure learning methods, and then multiple times Repeat the optimization process to get the optimal solution.

Description of drawings

Fig. 1 is the flow chart of the distance measure optimization method of maximizing the average precision rate mean value of the present invention;

Fig. 2 is a schematic diagram of the convergence of MAP with the number of optimization algorithm iterations in the process of optimizing the retrieval precision index MAP of the present invention;

Fig. 3 is the recall-precision rate curve that the distance measure obtained by the present invention and other distance measure optimization methods is used for retrieval;

Fig. 4 is a curve diagram of the average precision rate of four kinds of distance measures when the return image is 50 pieces;

Fig. 5 is an example of using the distance measure optimized by the present invention for brain tumor T1 weighted enhanced MRI image disease retrieval

Detailed ways

Fig. 1 shows the specific process of the distance measure optimization method of maximizing the average precision rate mean value of the present invention, comprising the following steps:

(1) Obtain an image database containing a collection of manually labeled query image-to-be-queried image pairs; the image database is composed of images or image region features, and image categories.

(2) Approximate MAP with a smooth function, convert it into an objective function and add a regularization term, so that the objective function is continuously differentiable; the initial solution of the transformation matrix can be a random matrix or other faster distance measure learning methods Estimated transformation matrix. The process of approximating the MAP is: for a given query image, the sequence number of any image to be queried is smoothly approximated using a Sigmoid function, and then the smooth approximation of the MAP is obtained.

The sequence number of the image to be queried is determined by comparing the distance between the image to be queried and all other images to be queried and the query image.

(3) Use the query image in the image database-the image to be queried and use the stochastic gradient descent algorithm to optimize the objective function, repeat the optimization process, and take the solution that maximizes the MAP as the optimal linear transformation matrix;

(4) The distance measure between images is used to retrieve images, and the optimal linear transformation matrix in step (3) includes two ways: one is to use the linear transformation matrix to transform the image features in the image database first , and then use the Euclidean distance of the transformation feature to define the distance measure between images, so as to perform image query; the other is to use the linear transformation matrix to define the Mahalanobis distance as the distance measure of the image for image query.

In the following, the working principle and steps of the present invention will be described in combination with the T1 weighted enhanced MRI image retrieval problem of the brain.

Step 1. Read the MRI image, the pathological type of the tumor in the image, and the outline of the lesion manually drawn by the doctor from the image database, and extract features such as grayscale, texture, shape, and edge of the lesion area, and the feature vector is expressed as x _i . Define images containing the same type of tumors as correlated images, otherwise as irrelevant images. The task of image retrieval is to return images of the same pathological type as the lesion area in the query image in the database to the user.

Step 2, since MAP is related to the ordering of the images to be queried, firstly determine and approximate the ordering number of each image to be queried according to the distance between the image to be queried and the image to be queried. Let L be a d×D (d≤D) real number matrix, positive semi-definite matrix W=L ^T L, then the Mahalanobis distance (square) between x _i and x _j is

d _ij ＝||Lx _i -Lx _j || ² ＝(xi _{-x j} ) ^T L ^T L( _xi -x _j )＝( _xi -x _j ) ^T W( _xi -x _j ),

Here ^T represents the transpose operation of the matrix. Let the query feature vector be x _q , the query-to-query pair is (x _q , { _xi , i=1, 2, ..., N}), where N is the total number of images to be queried, and the eigenvector to be queried x _i The sort sequence number of can be expressed as

$\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; qi</span>}}<span\; class="notranslate">\; ></span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; qk</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ,</span>$

Wherein Δd _ik =d _qi -d _qk , 1{} is an indicator function. Since the indicator function is discontinuous and non-differentiable, the sequence number π( _xi ) as a function of the distance d _qi or L is also discontinuous and non-differentiable. The indicator function can be a continuously differentiable Sigmoid function, denoted as S(Z). The smooth approximation of the sequence number π(xi ₎ is

其中rel(x_i)∈{0，1}表示两级相关的标号，N⁺为与查询图像相关的图像总数，

MAP为平均查准率在所有查询对上的平均。AP可写成如下形式The average precision rate (Average Precision, AP) of retrieval precision index is defined as

where rel( _xi )∈{0, 1} represents the label of two-level correlation, N ⁺ is the total number of images related to the query image,

MAP is the average of the average precision over all query pairs. AP can be written as follows

$\mathrm{<span\; class="notranslate">\; AP</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; N</span>}}^{<span\; class="notranslate">\; +</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; rel</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; rel</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; rel</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

替代π(x_i)，并再次用Sigmoid函数逼近指示函数，AP的平滑逼近为use

Substituting π( _xi ), and again using the Sigmoid function to approximate the indicator function, the smooth approximation of AP is

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; N</span>}}^{<span\; class="notranslate">\; +</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; rel</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{\mathrm{<span\; class="notranslate">\; rel</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; rel</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; )</span>}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

The regularization term of the transformation matrix L is denoted as Reg(L). Reg(L) can take trace(L ^T L), where trace(M) represents the trace of matrix M; Reg(L) can also take other norm forms of L.

Maximizing MAP is equivalent to minimizing 1-MAP. Define the average precision loss function:

${\mathrm{<span\; class="notranslate">\; loss</span>}}_{\mathrm{<span\; class="notranslate">\; AP</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; ,</span>$

The objective function defined by the present invention has the following form:

R(L)=Loss _AP (L)+γReg(L),

where γ is a weight coefficient used to control the balance between the loss function and the regularization term. R(L) is continuously differentiable.

The distance measure optimization problem of the present invention is expressed as:

$\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; D.</span>}}}{\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; min</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Where M is the total number of query-to-query image pairs, and R _m (L) is the objective function on the mth query-to-query image pair.

t＝1，2，...，T为迭代次数，T为设定的最大迭代次数，η_t为第t次迭代的步长；重复迭代，直至达到最大迭代次数或解收敛条件。多次重复上述过程，选取使检索精度指标最大的解作为L^*。如取trace(L^TL)作为正则化项，则梯度g_t为：Step 3, first estimate the initial solution L ₀ , _which can be a d×D random matrix or a solution obtained by other distance measure learning methods. In the tth iteration, the query-to-be-queried pair (x _q , { _xi , i=1, 2, ..., N _t }) _t is randomly generated from the image database, and R(L _t ) is calculated in the query For the gradient g _t about L _t above, update L _t =L _t-1 -η _t g _t , where

t=1, 2,..., T is the number of iterations, T is the maximum number of iterations set, η _t is the step size of the tth iteration; repeat iterations until reaching the maximum number of iterations or solving the convergence condition. The above process is repeated many times, and the solution that maximizes the index of retrieval accuracy is selected as L ^* . If trace(L ^T L) is used as the regularization term, the gradient g _t is:

${\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; loss</span>}}_{\mathrm{<span\; class="notranslate">\; AP</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}$

通过链式法则得到。The partial derivative of the loss function with respect to L _t

obtained by the chain rule.

Algorithm parameters α and γ can be adjusted through the cross-check method. Empirically, α ranges from 1 to 10, and γ ranges from 0.0001 to 0.01 to achieve satisfactory results. The step size of gradient descent can be η _t = η ₀ exp(-2t/T), t is the current number of iterations, and the step size can also be adjusted in other ways. FIG. 2 shows the convergence of MAP with the number of optimization algorithm iterations in the process of optimizing the retrieval accuracy index MAP in the present invention.

Step 4, for the linear transformation L ^* obtained in step 3, there are two equivalent ways to apply to image retrieval. One is to use L ^* to map the original feature vector to a new feature space, and then use the standard Euclidean distance as the image similarity measure; the other is to directly use L ^* to define the Mahalanobis distance as the image similarity measure for retrieval, the former It can reduce the storage space required by features and speed up image retrieval.

Fig. 3 is the recall-precision rate curve of the distance measure obtained by the present invention and other distance measure learning methods for retrieval, wherein the experimental data are T1 weighted enhanced MRI images of the brain, and images containing the same type of tumor are related images, Otherwise, it is an irrelevant image. The distance measures used for comparison include standard Euclidean distance, Mahalanobis distance learned by Large Margin Neighbor Classification (LMNN) and Local Fisher Discriminant Analysis (LFDA) methods. It can be seen that the method of the present invention can achieve a higher MAP, which is better than the Euclidean distance and the other two distance measure learning methods.

Figure 4 shows the average precision curves of the four distance measures when 50 images are returned, and the image data used is the same as that in Figure 3. In the distance measure optimization method in the present invention, when returning the first 5-50 images, the average precision rate is higher than the other three distance measures.

Fig. 5 is the example that uses the distance measure that the present invention obtains to be used for brain tumor T1 weighted enhanced MRI image disease retrieval, the image in the upper left corner among the figure is query image, and the representation retrieval of solid line frame (white line frame) Images (indicating the same type of tumor), those with a dotted line frame (white dotted line frame) indicate irrelevant images retrieved (indicating different tumor types), and the outline of the tumor area in the figure has been drawn manually. The above experimental data show that the distance measure obtained by the present invention can achieve better retrieval performance than some other distance measure learning methods.

Embodiments of the present invention are not limited thereto. Other similar MAP retrieval accuracy indicators defined by the sorting numbers of images to be queried, such as Prec@k and NDCG, can also be approximated using formulas and methods similar to the above, and then use the method of the present invention Optimization method is solved, not enumerating one by one here; Other optimization techniques and step size adjustment methods based on gradient descent, such as conjugate gradient descent algorithm can also be used to realize the object of the present invention; According to the above-mentioned content of the present invention, according to the art Without departing from the above-mentioned basic technical idea of the present invention, the present invention can also make other equivalent modifications, replacements or changes, all of which fall within the protection scope of the present invention.

Claims (6)

1. One kind the maximization average precision ratio average the distance measure optimization method, may further comprise the steps:

   (1) obtains the image data base that comprises query image-image pair set to be checked;

   (2) adopt smooth function that MAP is approached, be converted into objective function and add regularization term, make that objective function is continuously differentiable;

   (3) query image-image to be checked in the use image data base is right, adopts the method that descends based on gradient to be optimized to objective function, and repeats optimizing process, gets the matrix of a linear transformation of separating the conduct optimum that makes the MAP maximum;

   (4) image pitch comprises dual mode from obtaining of estimating: the optimum linearity transformation matrix in the usefulness step (3) is to the advanced line translation of the characteristics of image in the image data base, again with the distance measure between the Euclidean distance definition image of transform characteristics; Perhaps use the optimum linearity transformation matrix in the step (3) to define mahalanobis distance as the distance measure between image.
2. 2. the distance measure optimization method of the average precision ratio average of maximization according to claim 1 is characterized in that: the image data base in the described step (1) is made of image or image-region feature, image category.
3. 3. the distance measure optimization method of the average precision ratio average of maximization according to claim 1, it is characterized in that: the inquiry in the described step (1)-right set of image to be checked is that whether foundation comprises same anatomical, the same type focus determines that image to whether similar, marks.
4. 4. the distance measure optimization method of the average precision ratio average of maximization according to claim 1 is characterized in that: the transformation matrix that obtains with stochastic matrix or other distance measure learning methods in the described step (2) is as the initial solution of the matrix of a linear transformation.
5. 5. the distance measure optimization method of the average precision ratio average of maximization according to claim 1, it is characterized in that: the process of in the described step (2) MAP being approached is: to given query image, the ordering sequence number of arbitrary image to be checked uses the Sigmoid type function smoothly to approach, and then obtains smoothly approaching of MAP.
6. 6. the distance measure optimization method of the average precision ratio average of maximization according to claim 1 is characterized in that: adopting at random in the described step (3), gradient descent algorithm comes the optimization aim function.

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