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Parameter-dependent connected component of gray images and image understanding, segmentation and stereo correspondence

Yang Wang, University of Nebraska - Lincoln

Abstract

In this paper a new definition for connected components of gray images is introduced. The proposed definition takes into account both the gray values of the pixels and the differences of the gray values of the neighboring pixels. It depends on two parameters $\epsilon$ and $\delta$ and so we call it an ($\epsilon ,\ \delta$)-component. We develop an algorithm to partition an image into ($\epsilon ,\ \delta $)-components and give implementations of it on several images using different values of $\epsilon$ and $\delta$. Then we explore applications of the concept of ($\epsilon ,\ \delta$)-component in various areas of computer vision. First we propose a method for image understanding by applying the theory of ($\epsilon ,\ \delta$)-components. We study various properties of an image at the connected component level, from the low level vision to an intermediate level vision. Using the information obtained from various component histograms and certain pre-knowledge, we describe how to select suitable values of the parameters so that an object in a gray image may be represented by an ($\epsilon ,\ \delta$)-component. Segmentation of the object could be done by locating the corresponding component. Next we propose a new definition of digital connectivity for gray images on a 2D space for arbitrary grid systems. We extend a digital version of the Jordan curve theorem and its converse which was proved earlier by Rosenfeld (1970) for the rectangular grid system. We also extend in two directions the concept of well-composed sets introduced by Latecki, Eckhardt and Rosenfeld (1995). Finally, we propose a new feature-based method for stereo matching, which uses the boundaries of ($\epsilon ,\ \delta$)-components as the matching primitives. Under certain assumptions, there is a one-to-one correspondence between subsets of the points on the boundaries of ($\epsilon ,\ \delta $)-components of stereo pairs. This correspondence can be identified using the epipolar geometry. Using matched boundaries, we can identify the corresponding connected components determined by the boundaries and by changing the values of the parameters, we obtain a hierarchical stereo correspondence method.

Subject Area

Computer science|Mathematics|Optics

Recommended Citation

Wang, Yang, "Parameter-dependent connected component of gray images and image understanding, segmentation and stereo correspondence" (1997). ETD collection for University of Nebraska-Lincoln. AAI9805529.
https://digitalcommons.unl.edu/dissertations/AAI9805529

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