Road pavement cracks detection has been a hot research topic for quite a long time due to
the practical importance of crack detection for road maintenance and traffic safety. Many …

" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

The computer vision and pattern recognition communities have recently witnessed a surge
of feature-based methods in object recognition and image retrieval applications. These …

Topological persistence has proven to be a key concept for the study of real-valued
functions defined over topological spaces. Its validity relies on the fundamental property that …

We present a clustering scheme that combines a mode-seeking phase with a cluster
merging phase in the corresponding density map. While mode detection is done by a …

In 2009, Chazal et al. introduced ϵ ϵ-interleavings of persistence modules. ϵ ϵ-
interleavings induce a pseudometric d_ I d I on (isomorphism classes of) persistence …

We study the problem of computing zigzag persistence of a sequence of homology groups
and study a particular sequence derived from the levelsets of a real-valued function on a …

We present an efficient and robust method for extracting curvature information, sharp
features, and normal directions of a piecewise smooth surface from its point cloud sampling …

Algorithms for persistent homology are well-studied where homomorphisms are induced by
inclusion maps. In this paper, we propose a practical algorithm for computing persistence …

Feature-based approaches have recently become very popular in computer vision and
image analysis applications, and are becoming a promising direction in shape retrieval …