Digital geometry in image processing by Jayanta Mukhopadhyay, (College teacher); et al

By Jayanta Mukhopadhyay, (College teacher); et al

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By Jayanta Mukhopadhyay, (College teacher); et al

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The paths Π1 (marked by ’*’) and Π2 (marked by ’#’) are both minimal while the path Π (marked by ’$’) is not minimal. Note that |Π∗1 |=|Π∗2 |=9 and |Π|=14. 1 Shortest Path Algorithm For a neighborhood set N (·), there may be infinitely many paths in Zn between u and v. Here, we formulate a shortest path tracing algorithm to trace one of the many shortest paths between the two points. Once the path has been traced, we analyze the algorithm to find the length of the shortest path. Without loss of generality, we assume that u = 0 and v = x, where x ∈ Σn .

Path-Dependent Neighborhoods and Distances . . . . . . . . . 1 Hyperoctagonal Distance . . . . . . . . . . . . . . . . 1 Necessary and Sufficient Condition for Metricity . . . . . . . . . . . . . . . . . . 2 Octagonal Distances in 2-D . . . . . . . . . . . . . . . 1 Best Simple Octagonal Distance . . . . . . 3 Weighted t-Cost Distance . . . . . . . . . . . . . . . . Hyperspheres of Digital Distances . . .

2 Special Cases of Hyperspheres in 2-D and 3-D . . . . . . . . . . . . . . . . . . . . . 6 Hyperspheres of Weighted t-Cost Distance . . . . . . . 1 Proximity to Euclidean Hyperspheres . . . Error Estimation and Approximation of Euclidean Distance . . 1 Notions of Error . . . . . . . . . . . . . . . . . . . . . 2 Error of m-Neighbor Distance . . . . . . . . . . . . . . 3 Error of Real m-Neighbor Distance . .

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