Research On Digital Image Classification Based On Persistent Homology

The application of topological characteristics based on persistent homology(PH)has long been a topic of interest in the burgeoning discipline of topological data analysis(TDA).In topological data analysis,persistent homology is a sophisticated instrument for determining,studying,and encoding effective multi-scale topological properties,and it is widely employed in digital picture classification of topological features based on persistent homology has always been an interesting topic in the emerging field of topological data analysis.Persistent homology is a sophisticated instrument to calculate,study and encode effective multi-scale topological features in topological data analysis,and it is increasingly used in digital image classification.There are two main research directions in traditional image matching,classification,and recognition:one is based on gray correlation,while the other is centered on feature representation.Previous image feature extraction research methods that utilize image subject matter pretty much exclusively extricate photo color histogram,texture function,version features,and municipal feature of picture embraced in current history.Provided that a single feature is inadequate for describing image information,this thesis suggests a topological feature fusion visual feature method for image classification technology research based on persistent homology.The main work is as follows:1.Using the persistent homology principle,topological feature descriptors on images can be extracted.In this research,we obtain the topology components of pictures at different scales and monitor the life spans of the those features using the algebraic topology concept on persistent homology.The robust topological constant,which may fully and precisely describe the topological features of the image,is extracted from the graph and presented in the persistent structure as the feature representation.2.Contrast Limited Adaptive Histgram Equalization(CLAHE)was used for image enhancement.The decorative features are extracted according to the characteristics of the set of data,as well as the feature values of Gray Level Co-Occurrence Matrix(GLCM)are employed to obtain them.Such characteristics can accurately reflect the homogeneity of the gray distribution of the image,the thickness of the appearance,the clarity of the picture,and the complexity of grain details.3.MNIST handwritten digit data set was used to study the properties related to persistent homology,and experiments were designed to verify the rotational invariance and global invariance of persistent homology,and multi-index comparison of complex filter flow and different feature descriptors was conducted.The topological features and texture features extracted from the rolling surface defect database published by Northeastern University were analyzed,and the multi-feature fusion method was applied to implement the test.In conformity to the experiment results,topological features obtained using persistent homology in combination with visual cues have a good classification effect in this type of weld fault data set.The main contribution of this thesis is to propose an image topological feature extraction method based on continuous homology,and combine it with GLCM image texture feature,which improves the accuracy of image classification by using their spatial and visual complementarity.The practical findings show that the suggested strategy performs well and that the categorization impact of feature engineering is greater compared to a feature space classification.