Abstract <p>Among the main tasks of computer vision, clustering can be singled out, since without it, it is impossible to create a completely independent model of image recognition. The neural network approaches that do the best job of solving this problem rely on a large training set, but even this is not enough to work reliably. Therefore, a method is needed that can solve computer vision problems at a more abstract level without huge training data. One such method is persistent homology. The use of persistent homology in image processing has a number of limitations, both from a computational and mathematical point of view. They can be solved by using persistent landscapes, which will reduce the number of features and also provide a mathematically correct way of comparison through the distance function. The paper compares various clustering methods that use features calculated from persistent landscapes as input parameters. As a result of the research, the use of persistent landscapes showed positive results, but not for all methods and parameters. It&#xa0;was found that the best results are shown by <i>k</i>-means and hierarchical classifiers for features calculated as the distance by the infinite norm. It is shown that clustering works more efficiently with a small number of classes. The possibility of using persistent landscapes to reduce the number of features from 48 to 92% is also demonstrated, which provides acceleration for image processing.</p>

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Using Persistent Landscapes in Image Processing

  • A. V. Abakumov,
  • S. V. Eremeev

摘要

Abstract

Among the main tasks of computer vision, clustering can be singled out, since without it, it is impossible to create a completely independent model of image recognition. The neural network approaches that do the best job of solving this problem rely on a large training set, but even this is not enough to work reliably. Therefore, a method is needed that can solve computer vision problems at a more abstract level without huge training data. One such method is persistent homology. The use of persistent homology in image processing has a number of limitations, both from a computational and mathematical point of view. They can be solved by using persistent landscapes, which will reduce the number of features and also provide a mathematically correct way of comparison through the distance function. The paper compares various clustering methods that use features calculated from persistent landscapes as input parameters. As a result of the research, the use of persistent landscapes showed positive results, but not for all methods and parameters. It was found that the best results are shown by k-means and hierarchical classifiers for features calculated as the distance by the infinite norm. It is shown that clustering works more efficiently with a small number of classes. The possibility of using persistent landscapes to reduce the number of features from 48 to 92% is also demonstrated, which provides acceleration for image processing.