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Recently a new feature representation framework based on a topological tool called persistent homology (and its persistence diagram summary) has gained much momentum. A series of methods have been developed to map a persistence diagram to a vector representation so as to facilitate the downstream use of machine learning tools. In these approaches, the importance (weight) of different persistence features are usually pre-set. However often in practice, the choice of the weight-functions hould depend on the nature of the specific data at hand. It is thus highly desirable to learn a best weight-function (and thus metric for persistence diagrams) from labelled data. We study this problem and develop a new weighted kernel, called WKPI, for persistence summaries, as well as an optimization framework to learn the weight (and thus kernel). We apply the learned kernel to the challenging task of graph classification, and show that our WKPI-based classification framework obtains similar or (sometimes significantly) better results than the best results from a range of previous graph classification frameworks on benchmark datasets.
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A Topological Graph-Based Representation for Denoising Low Quality Binary Images
Scanned images of patent or historical documents often contain localized zigzag noise introduced by the digitizing process; yet when viewed as a whole image, global structures are apparent to humans, but not to machines. Existing denoising methods work well for natural images, but not for binary diagram images, which makes feature extraction difficult for computer vision and machine learning methods and algorithms. We propose a topological graph-based representation to tackle this denoising problem. The graph representation emphasizes the shapes and topology of diagram images, making it ideal for use in machine learning applications such as classification and matching of scientific diagram images. Our approach and algorithms provide essential structure and lay important foundation for computer vision such as scene graph-based applications, because topological relations and spatial arrangement among objects in images are captured and stored in our skeleton graph. In addition, while the parameters for almost all pixel-based methods are not adaptive, our method is robust in that it only requires one parameter and it is adaptive. Experimental comparisons with existing methods show the effectiveness of our approach.
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- Award ID(s):
- 1748883
- PAR ID:
- 10166136
- Date Published:
- Journal Name:
- 2019 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW)
- Page Range / eLocation ID:
- 1788 to 1798
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICCVW.2019.00222
