arXiv subjects

Wanchen Zhao

Publications and source records attributed to Wanchen Zhao.

3 recordsLinked to original sources

arXiv2025

Continuous persistence landscapes

As the size of data increase, persistence diagrams often exhibit structured asymptotic behavior, converging weakly to a Radon measure. However, conventional vector summaries such as persistence landscapes are not well-behaved in this setting, particularly for diagrams with high point multiplicities. We introduce continuous persistence landscapes, a new vectorization defined on a special class of Borel measures, which we call q-tame measures. It includes both the persistence diagrams and their weak limits. Our construction generalizes persistence landscapes to a measure-theoretic setting, preserving the intrinsic structure of persistence measures. We show that this vector summary is bijective and L^1-stable under mild assumptions, and that the original measure can be uniquely reconstructed. This approach gives a more faithful description of the shape of data in the limit and provides a stable, invertible way to analyze topological features in large systems.

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arXiv2025

A rank-based distance for interval modules and Wasserstein stability of persistence landscapes

Barcodes and persistence diagrams have a canonical one-parameter family of distances called Wasserstein distances. These distances depend on a choice of distance for interval modules. The usual choices are all Lipschitz equivalent. We observe that they may be written in terms of the dimension function. We instead define a distance for interval modules using the rank function. The rank function contains the information of dimension function and unlike the dimension function, also contains information on persistence. Using this distance, we show that persistence landscapes are stable with respect to the 1-Wasserstein distance. This gives us a 1-Lipschitz embedding of persistence diagrams with the 1-Wasserstein distance into a Banach space given by an $L^1$ function space, and also provides a lower bound for the 1-Wasserstein distance. In addition, we give a stability theorem for the mapping from chains to barcodes. This result leads to a heuristic for truncating infinite bars.

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arXiv2024

Enhanced Unsupervised Image-to-Image Translation Using Contrastive Learning and Histogram of Oriented Gradients

Image-to-Image Translation is a vital area of computer vision that focuses on transforming images from one visual domain to another while preserving their core content and structure. However, this field faces two major challenges: first, the data from the two domains are often unpaired, making it difficult to train generative adversarial networks effectively; second, existing methods tend to produce artifacts or hallucinations during image generation, leading to a decline in image quality. To address these issues, this paper proposes an enhanced unsupervised image-to-image translation method based on the Contrastive Unpaired Translation (CUT) model, incorporating Histogram of Oriented Gradients (HOG) features. This novel approach ensures the preservation of the semantic structure of images, even without semantic labels, by minimizing the loss between the HOG features of input and generated images. The method was tested on translating synthetic game environments from GTA5 dataset to realistic urban scenes in cityscapes dataset, demonstrating significant improvements in reducing hallucinations and enhancing image quality.

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