This is an article using low rank matrix decomposition to make textile defect detection, the paper modifies the traditional LRR model, replaces the original mixed norm with the f norm, and a new name is called the least-squares regression under the guidance of transcendental knowledge, and there is no obvious difference in nature. I think the real point of this article is to build a template reference image, the basic idea is that the defect is only a small part of the textile image, then I randomly in the textile image to take blocks, it is possible to obtain a defect-free image block, using randomly obtained blocks to build the reference, as a defect-free textile image. This is different from the traditional textile defect detection needs "clean" template, but also in the future research can be used to learn from the place. This article works by a teacher at Dalian University of Technology, published on multimedia Tools and applications, in the computer field is a 3-zone SCI journal, if at about 1.3. Related work defect detection methods the existing defect detection techniques are divided into three categories: Model-based method, frequency-domain based method (Fourier transform, Gabor Transform, wavelet transform) and statistical-based method (in fact, spatial domain method). The following is a brief introduction to these methods. The model-based method is used to extract image texture features through model and parameter estimation techniques. The most common model-based approach is the Markov random field model, but I don't know exactly what this model does. Often see these few words, but exactly what, how to play a role in the need of my follow-up study. In general, model-based approach complexity is computationally high. Based on the frequency domain method, the textile image is first converted to the frequency domain, and then the characteristics are extracted by some energy criterion. In layman's words, it is the filtering technology in Digital image processing. It can be understood that textile images show a strong regularity, corresponding to the frequency domain should also have a fixed law, defects will destroy this regularity. Through the filtering technique, the "wave" corresponding to the defective part is mapped back to the space domain to realize the flaw detection. Based on the statistical method, it is also called the spatial domain statistic method, that is, the statistical method and the spatial domain method refer to the same kind of method when reading the literature. such as gray-scale co-occurrence matrix, LBP, statistical histogram, etc. belong to the spatial domain method, in short, the extraction of features in the spatial domain, the classification of features and other operations to achieve textile defects detection. Significance detection based on low rank representation the body of this article is based on the low-rank representation model (LRR). LRR model is Liu Guangan teacher in the doctoral stage of the model, now Liu teacher in Nanjing University of Information engineering professor, very powerful. Teacher Liu's homepage: http://web2.nuist.edu.cn:8080/jszy/Professor.aspx?id=1990 original paper can be referenced robust subspace segmentation by Low-rank RepresentatIon This paper, if too laborious can be on the internet to search for teacher Liu's doctoral dissertation. The basic model is:
algorithmimage Segmentation and feature extractionFirst, the image I is divided into small pieces of m*m, each small block is recorded as B, and then each of the small pieces of each pixel in the calculation of a 8-dimensional Texton feature, take a small block of all the pixels of the characteristics of the average value as the current block characteristics, the feature can see what is textons? This article is not very good to read. Finally constitute a 8*n-dimensional characteristic matrix, 8 refers to each block has extracted 8-dimensional special system features, n refers to the number of blocks. All of this can be expressed as the following formula:
Textile defect Detection ModelThe LRR model is listed earlier, and you can see that in the LRR model, the original feature matrix X is reconstructed by multiplying itself by a coefficient matrix Z plus the noise matrix E, where Z has a low rank property. At the same time, E is sparse, because the defect occupies only a small part of the entire textile, and the defect is equivalent to noise, so the matrix E is sparse. On this basis, the definition of an irregular map (irregularity maps) is as follows:
indicates that column I is the possibility of a defect. It can be understood that we are the extraction feature for each block, a column of the corresponding matrix, the more than 0 elements in the column, that is, s (Bi), the greater the column, the more "significant", the more likely the defect block. PG-LSRThis is the innovation point of this article, in fact, not too strong innovation. Although the LRR model can roughly identify defects, but the nuclear norm is not smooth (this is the article, but I do not know why not smooth, not to say that the nuclear norm has been replaced rank is to avoid rank of non-convex?) It is time-consuming to compute the SVD for the LRR model, so the author proposes to replace the norm in the model with the more easily solved F-norm, which is the square sum of the elements, which is the so-called least-squares regression in the author's title. So the model presented by the author is as follows:
at this point, it only embodies the least-squares regression in the title, but the prior knowledge in the title has not been reflected. To get a clearer view of the irregular map, the author adds a priori knowledge to the model to get the following model:
here W is a weight matrix. The basic idea is that the above model is the minimization model, if it is considered that a piece is a defect-free block, that is, the corresponding column in E (Bi) is very small, the list of more than 0 elements, then I will be the location of the w corresponding to the larger. If the current block is a defective block, set the position of the w corresponding to a smaller location. How do you determine if the current block is most likely a defect or a defect-free one? This is the building block of referenced images, which I think is the best part of this article. Building a reference imageNote that our detection object is each image block, each image block corresponds to a eigenvector. Therefore, in order to construct the guidance matrix W, we need to calculate a reference eigenvector corresponding to the defect-free feature block. The basic idea is that the defect is only a small part of the textile image, then I randomly take the block to get the small piece is likely to be a defect-free block. The s blocks are randomly selected from the image, then the mean values of the eigenvector of the s image block are used to make reference eigenvectors. This process repeats k times, so we can get K eigenvectors. The last feature vector can be solved by the following model
The reference eigenvector can be used to construct the weights matrix by using the reference eigenvectors. If the new image block has a large distance from the reference eigenvector, then we think the block is a defective block. Conversely, if the new image block corresponding to the feature vector and the reference eigenvector distance is small, then we think that the image block is not defective. The distance between the characteristic vector and the reference eigenvector is recorded as Pi, according to the preceding description, the weights matrix can be constructed as follows, which embodies the prior knowledge in the title:
The larger the distance, the defect block, the smaller the weight, the smaller the distance is the defect-free block, the greater the weight value. This is exactly what the article should be all about. The purpose of this blog post is to learn how to construct a defect-free reference using random blocks, while at the same time it may help students who read this article understand better. If you have any questions, you can send an email to[email protected] to talk and learn from each other.
Fabric defect inspection using prior knowledge guided least squares regression
