A learning-based Tchebichef moment invariant feature extraction method

Abstract

The present invention discloses a learning-based Tchebichef moment invariant feature extraction method, which relates to technical fields such as image processing, computer vision, and machine learning. The specific steps are: 1) rotating the dataset image to the principal axis and moving the image coordinate origin to the image centroid to obtain a normalized image; 2) constructing a scale space for the normalized image, calculating and fusing the Tchebichef rectangles of the multi-scale images into moment features that are invariant to geometric transformations; 3) utilizing a two-stage feature learning strategy to effectively reduce the dimensionality of the moment features to obtain the final Tchebichef moment invariants; 4) feeding the moment invariants as features into an SVM classifier for subsequent tasks such as image classification or invariance recognition. The Tchebichef moment invariant recognition proposed by this method has good performance and low computational complexity, and can be applied to real-time scenarios such as face recognition and object recognition, thus having practical significance.

Description

Technical Field

[0001] The present invention relates to a learning-based Tchebichef moment invariant feature extraction method, and belongs to the technical fields of digital image processing, computer vision, machine learning, and the like. Background Art

[0002] With the rapid development of network and multimedia technologies, the generation, transmission, and downloading of images have become extremely simple. In many cases, images can be used to express information such as text in a concise and clear manner. Therefore, the use of images not only adds color to people's lives but also effectively improves work efficiency. However, its negative impact has also become apparent. People can download any image at will and perform operations such as translation, scaling, and rotation on it as needed. This makes applications such as image recognition extremely difficult because the original image is susceptible to one or more of these attacks. To address these issues, it is necessary to construct features that can express the objective information of the original image. This requires that even if the original image is affected by geometric transformations, the extracted image features must remain consistent with the original image features. In other words, the features must be unaffected by geometric transformations and independent of the size, position, and rotation angle of the digital image. Image moments are transformation models that map image functions to specific basis functions. Low-order moments can extract low-frequency information such as image contours, while high-order moments can extract image details. Image moments can be divided into non-orthogonal and orthogonal moments based on whether their basis functions are orthogonal. Orthogonal moments have superior image representation capabilities. Among orthogonal moments, the Tchebichef moments are discretized, and their basis functions are scoped to fit square N×N images. Image moments themselves lack complete geometric invariance, but due to their outstanding image representation capabilities, constructing invariants based on image moments has attracted widespread attention.

[0003] There are currently three common methods for constructing moment invariants. The first is through normalized images or normalized moments. This method is simple and easy to implement, but the normalization process requires resampling and renormalization of the image, which can cause large errors in the results. The second is the indirect method, which uses invariant geometric moments or invariant complex moments to construct moment invariants. This method solves the defects of the first method, but due to the non-orthogonality of the geometric moment or complex moment basis functions, the constructed moment invariants have a large amount of information redundancy and poor robustness to noise. In addition, its time complexity is also relatively large. The third is the direct method, which constructs moment invariants based on the relationship between the moment set of the original image and the moment set of the image subjected to geometric transformation. This method is better than the first two methods, but its derivation process is very complicated. Summary of the Invention

[0004] Because the three common methods mentioned above each have their own drawbacks, this paper proposes a novel method for extracting structural information from images by simulating scale transformations in scale space and implementing Tchebichef moment invariants based on a feature learning strategy. This method extracts Tchebichef moment invariants with low dimensionality and strong resistance to geometric transformations. This invariant can achieve high classification accuracy on mixed datasets with geometric transformations and exhibits good noise robustness.

[0005] In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a learning-based Tchebichef moment invariant feature extraction method, characterized by comprising the following steps:

[0006] (1) The dataset image is rotated to the principal axis and the image coordinate origin is moved to the image center of mass to obtain a normalized image.

[0007] (2) Construct the scale space of the normalized image, calculate and fuse the multi-scale image rectangles into moment features that are invariant to geometric transformations.

[0008] (3) Using a two-stage feature learning strategy, the moment features are reduced in dimension to obtain the final moment invariant.

[0009] (4) The moment invariants are fed as features into the SVM classifier for subsequent tasks such as image classification or invariance recognition.

[0010] Specifically, the spindle in step (1) and image centroid The calculation formula is as follows:

[0011]

[0012]

[0013] The M in the formula represents the geometric moment, which is calculated as follows: Where f(x,y) represents the image function, and p and q represent the order.

[0014] Specifically, the process of constructing the scale space in step (2) is a process of continuously filtering the original image with a Gaussian kernel function with gradually increasing standard deviation σ, thereby obtaining a scale space formed by multiple Gaussian filtered images; after the scale space is constructed, the first P-order Tchebichef moments of the image in the scale space are calculated and connected in series to obtain a multi-scale Tchebichef moment feature with geometric transformation invariance.

[0015] More specifically, each image in the scale space is calculated as follows:

[0016]

[0017] Among them, I(x,y) represents the original image, l i (x, y) represents the scale image of the i-th layer in the scale space, S represents the number of layers in the scale space, * represents the filtering operation, σ is the standard deviation of the Gaussian kernel function, and G represents the Gaussian kernel function. The form of G is as follows:

[0018]

[0019] x represents the horizontal coordinate, y represents the vertical coordinate, and (x, y) represents the coordinate position of a point.

[0020] More specifically, given an image function f(x,y) of size N×N, the nth and mth order normalized Tchebichef moments T nm is defined as follows:

[0021]

[0022]

[0023] in represents the normalized discrete Tchebichef polynomial of order n, ρ is a square norm independent of x, and k represents any value of order 0 to n.

[0024] After calculating the first P-order Tchebichef moments, the Tchebichef moments of each image in the scale space are fused to obtain the multi-scale Tchebichef moment MSTM:

[0025]

[0026] is the first P-th order Tchebichef moment of image I and [;] represents the concatenation operation of the first P-order Tchebichef moments of images of different scales.

[0027] Specifically, the two-stage feature learning strategy in step (3) includes feature pre-learning and feature selection. The top 25% of images of each category in the image library are used to participate in the feature pre-learning process, the average Tchebichef moment is calculated, the variance ratio DVar is arranged in descending order to obtain a one-dimensional feature index, and the feature index is passed to the feature selection stage; the feature selection stage first obtains the average Tchebichef moment of the image, then takes the index value of the first t% of the feature index, and extracts the feature value of the corresponding index in the average Tchebichef moment to form a learning-based Tchebichef moment invariant.

[0028] More specifically, the feature pre-learning includes the following steps:

[0029] (1) First, the average value of the MSTM of each image at different scales is calculated to obtain the average Tchebichef moment, which is represented by MTM.

[0030] (2) Take the mean of the MTM of the same class of images to obtain the intra-class mean of the MTM of each class of images, and use To express; at the same time, calculate the intra-class variance of MTM for each class of images, using express;

[0031] (3) According to each category Calculate the inter-class variance of MTM interVar At the same time, for each category Find the mean and calculate the mean variance MTM within the MTM class intraVar ;

[0032] (4) The variance ratio DVar obtained by the following formula is arranged in descending order to obtain the one-dimensional feature index:

[0033]

[0034] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor implements the steps of the above-mentioned learning-based Tchebichef moment invariant feature extraction method when executing the computer program.

[0035] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the above-mentioned learning-based Tchebichef moment invariant feature extraction method.

[0036] The advantages and beneficial effects of the above solution of the present invention are as follows:

[0037] This invention utilizes techniques such as image processing, computer vision, and machine learning to achieve the task of extracting moment invariant features. This method is a learning-based approach that concatenates Tchebichef moments of multi-scale images to generate an MSTM. The MSTM uses a two-stage feature learning strategy to obtain Tchebichef moment invariants. Using an SVM classifier for invariant recognition or classification in the presence or absence of noise can achieve good results. This invention has the following advantages:

[0038] (1) Use MATLAB tools to write and run code, which is low cost;

[0039] (2) The calculation of image moments is converted into the calculation of vectors and matrices, and a recursive method is used to avoid the factorial terms of the image moment basis function to accelerate the feature extraction task.

[0040] (3) Using a simple and effective feature learning strategy, the tasks that are useful for subsequent tasks are retained, effectively reducing the feature dimension while ensuring the moment invariant image recognition capability.

[0041] (4) The method for constructing moment invariants proposed in the present invention is universal and can be used to extract the invariant features of all image moments.

[0042] (5) High recognition accuracy can be achieved on both geometric transformation datasets and noisy datasets. In most cases, higher correct classification percentages (CCPs) can be obtained than other methods.

[0043] (6) It can be applied to practical scenarios such as face recognition and target recognition, and has important practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a system flow chart of the present invention;

[0045] Figure 2 It is the construction process of multi-scale Tchebichef moments;

[0046] Figure 3 It is the dimensionality reduction process of the feature learning strategy. DETAILED DESCRIPTION

[0047] The following will describe the technical solutions in the embodiments of the present invention in detail with reference to the accompanying drawings. The described embodiments are only a part of the embodiments of the present invention.

[0048] System flow chart as follows Figure 1 As shown, a learning-based Tchebichef moment invariant feature extraction method includes the following steps:

[0049] Step 1: Rotate the dataset image to the principal axis and move the image coordinate origin to the image center of mass to obtain a normalized image; the calculation formulas of the principal axis and the image center of mass are related to the geometric moment, and the p- and q-order geometric moments M pq The definition is as follows:

[0050]

[0051] f(x,y) represents the image function, p and q represent the order, x represents the horizontal coordinate, y represents the vertical coordinate, and (x,y) represents the coordinate position of a point.

[0052] Low-order geometric moments are mainly used to calculate information such as center of gravity and shape. and image centroid The calculation formula is as follows:

[0053]

[0054]

[0055] Step 2: Construct the scale space of the normalized image, calculate and fuse the multi-scale image rectangles into a multi-scale Tchebichef moment feature with geometric transformation invariance. The specific steps are as follows:

[0056] In reality, objects can transition from large to small scales as they move closer to the observer. Scale space can simulate multi-scale representations of objects. The process of constructing a scale space is to continuously filter the original image with a Gaussian kernel function with gradually increasing standard deviation σ. This operation yields a scale space formed by multiple Gaussian-filtered images. The present invention uses the following formula to generate each image in the scale space.

[0057]

[0058] Among them, I(x,y) represents the original image, l i represents the scale image of the i-th layer in the scale space, S represents the number of layers in the scale space, * represents the filtering operation, σ is the standard deviation of the Gaussian kernel function, G represents the Gaussian kernel function, and the form of G is as follows:

[0059]

[0060] After the scale space of the normalized image is constructed, in order to extract stable image structure information, it is necessary to calculate the first P-order Tchebichef moments of the multi-scale image and concatenate them to obtain multi-scale Tchebichef moment features with geometric transformation invariance. The entire process of generating multi-scale Tchebichef moments is as follows: Figure 2 As shown. For a given image function f(x,y) of size N×N, the nth and mth order normalized Tchebichef moments T nm is defined as follows:

[0061]

[0062]

[0063] in represents the normalized discrete Tchebichef polynomial of order n. ρ is a square norm that is independent of x, and k represents any value of order 0 to n.

[0064] After calculating the first P-order Tchebichef moments, the Tchebichef moments of each image in the scale space are concatenated to obtain the multi-scale Tchebichef moment MSTM, whose feature dimension is S×K:

[0065]

[0066] is the first P-th order Tchebichef moment of image I and [;] represents the concatenation operation of the first P-order Tchebichef moments of images of different scales.

[0067] Step 3: Use a two-stage feature learning strategy to effectively reduce the dimension of the moment features to obtain the final moment invariant, which includes the following steps:

[0068] Assuming that the number of scale space layers S or the maximum order of the Tchebichef moment is large, the dimension of the MSTM finally generated in the second step will also be large. The feature dimension is also a factor that needs to be considered in feature extraction. Too large a dimension will lead to a long feature extraction time and feature classification time. In order to effectively reduce the feature dimension of the MSTM invariant, the present invention proposes a two-stage feature learning strategy, which effectively reduces the dimension while maintaining the feature recognition ability to obtain the final Tchebichef moment invariant. The feature learning strategy includes two stages: feature pre-learning and feature selection. The specific process is as follows: Figure 3 shown.

[0069] The first stage of pre-learning is to use the top 25% of images in each category in the image library. First, the average value of the MSTM of each image at different scales is calculated to obtain the average Tchebichef moment, which is represented by MTM.

[0070]

[0071] Then take the mean of the MTM of the same type of images to get the intra-class mean of the MTM of each type of image, and use To express; at the same time, calculate the intra-class variance of MTM for each class of images, using express;

[0072]

[0073]

[0074] represents the intra-class mean of the average Tchebichef moment MTM of the i-th class, represents the mean Tchebichef moment MTM of the m-th image of the i-th class.

[0075] Then, according to each category Calculate the inter-class variance of MTM interVar At the same time, for each category Find the mean and calculate the mean variance MTM within the MTM classintraVar ;

[0076]

[0077]

[0078] Finally, the variance ratio DVar obtained by the following formula is sorted in descending order to obtain the one-dimensional feature index and the feature index after descending order is passed to the feature selection stage.

[0079]

[0080] During the feature selection phase, for each image in the database, the average MSTM at different scales is calculated to obtain the MTM. The index values ​​of the first t percent of the feature indexes obtained during the feature pre-learning phase are then taken and the feature values ​​of the corresponding indexes in the MTM are extracted to form a learning-based Tchebichef moment invariant. The dimension of this invariant is reduced from S×K of the MSTM to 1×(K×t%), but its image recognition capability is not reduced. This is because the MSTM and MTM contain redundant information that is not useful for classification. The dimensionality reduction method of this invention eliminates image information that is redundant for subsequent tasks, retaining information that is more useful for tasks such as classification.

[0081] Step 4: Send the moment invariant as a feature to the SVM classifier for subsequent tasks such as image classification or invariance recognition.

[0082] Experimental methods:

[0083] In the geometric transformation invariance verification experiments and image classification experiments, a 1:1 training set and test set strategy was adopted for the datasets used, and the average of the 100 classification results was used as the final result. During the 100 classification processes, half of the images in each category in the database were randomly selected as the training set, and the other half as the test set.

[0084] The first step is to construct a normalized image scale space, fuse the first P-order Tchebichef moments of each image in the scale space to obtain a multi-scale Tchebichef moment feature with geometric transformation invariance, and use a two-stage feature learning strategy to reduce the dimension to obtain the final moment invariant feature.

[0085] Step 2: Input the moment invariant features and corresponding label information of the training set images into the SVM, run the Matlab program, first train the optimal classifier parameter combination, and obtain the final model.

[0086] Step 3: Use the trained model to test the test set and get the correct classification percentage.

[0087] Experiments show that, compared with existing moment invariants, the highest classification accuracy is achieved on scale transformation datasets and geometric transformation mixed datasets, and the highest classification results are also achieved on the original datasets. In addition, under most Gaussian white noise and salt and pepper noise conditions, the learning-based Tchebichef moment invariant outperforms the existing moment invariants.

[0088] The above embodiments should be understood as merely illustrating the present invention and not as limiting the scope of protection of the present invention. After reading the contents of the present invention, technicians may make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A learning-based Tchebichef moment invariant feature extraction method, characterized in that: The following steps are involved: (1) Rotate the dataset image to the principal axis and move the image coordinate origin to the image center to obtain a normalized image; (2) Construct the scale space of the normalized image, calculate and fuse the multi-scale image rectangles into moment features that are invariant to geometric transformations; The process of constructing the scale space is to continuously filter the original image with a Gaussian kernel function with gradually increasing standard deviation σ, and obtain a scale space formed by multiple Gaussian filtered images. After the scale space is constructed, the first P-order Tchebichef moments of the image in the scale space are calculated and concatenated to obtain a multi-scale Tchebichef moment feature with geometric transformation invariance. (3) Using a two-stage feature learning strategy, the moment features are reduced in dimension to obtain the final moment invariant; the two-stage feature learning strategy includes feature pre-learning and feature selection, using the top 25% of images of each class in the image library to participate in the feature pre-learning process, calculating the average Tchebichef moment, sorting the variance ratios DVar in descending order to obtain a one-dimensional feature index, and passing the feature index to the feature selection stage; In the feature selection stage, the average Tchebichef moment of the image is first obtained, and then the index value of the first t% of the feature index is taken, and the feature value of the corresponding index in the average Tchebichef moment is extracted to form the Tchebichef moment invariant based on learning; (4) The moment invariants are fed as features into the SVM classifier for image classification or invariance recognition.

2. The learning-based Tchebichef moment invariant feature extraction method according to claim 1, characterized in that: The spindle described in step (1) and image centroid The calculation formula is as follows: The M in the formula represents the geometric moment, which is calculated as follows: Where f(x,y) represents the image function, and p and q represent the order.

3. The learning-based Tchebichef moment invariant feature extraction method according to claim 1, characterized in that: Each image in the scale space is calculated as follows: Among them, I(x,y) represents the original image, l i (x, y) represents the scale image of the i-th layer in the scale space, S represents the number of layers in the scale space, * represents the filtering operation, σ is the standard deviation of the Gaussian kernel function, and G represents the Gaussian kernel function. The form of G is as follows: x represents the horizontal coordinate, y represents the vertical coordinate, and (x, y) represents the coordinate position of a point.

4. The learning-based Tchebichef moment invariant feature extraction method according to claim 1, characterized in that: Given an image function f(x,y) of size N×N, the normalized Tchebichef moment T of order n and m nm is defined as follows: in represents the n-th order normalized discrete Tchebichef polynomial, ρ is a square norm independent of x, and k represents any value of order 0 to n. After calculating the first P-order Tchebichef moments, the Tchebichef moments of each image in the scale space are fused to obtain the multi-scale Tchebichef moment MSTM: is the first P-th order Tchebichef moment of image I and [;] represents the concatenation operation of the first P-order Tchebichef moments of images of different scales.

5. The learning-based Tchebichef moment invariant feature extraction method according to claim 1, characterized in that: The feature pre-learning includes the following steps: (1) First, the average value of the MSTM of each image at different scales is calculated to obtain the average Tchebichef moment, which is represented by MTM. (2) Take the mean of the MTM of the same class of images to obtain the intra-class mean of the MTM of each class of images, and use To express; at the same time, calculate the intra-class variance of MTM for each class of images, using express; (3) According to each category Calculate the inter-class variance of MTM interVar At the same time, for each category Find the mean and calculate the mean variance MTM within the MTM class intraVar ; (4) The variance ratio DVar obtained by the following formula is arranged in descending order to obtain the one-dimensional feature index:

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the steps of the learning-based Tchebichef moment invariant feature extraction method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the learning-based Tchebichef moment invariant feature extraction method according to any one of claims 1 to 5 are implemented.

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