| 1. |
- Nagy, Benedek, et al.
(författare)
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Distance Transform Based on Weight Sequences
- 2019
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Ingår i: DGCI 2019: Discrete Geometry for Computer Imagery. - Switzerland AG : Springer. - 9783030140847 - 9783030140854 ; , s. 62-74
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Konferensbidrag (refereegranskat)abstract
- There is a continuous effort to develop the theory and methods for computing digital distance functions, and to lower the rotational dependency of distance functions. Working on the digital space, e.g., on the square grid,digital distance functions are defined by minimal costpaths, which can be processed (back-tracked etc.) without any errors or approximations. Recently, digital distance functions defined by weight sequences, which is a concept allowing multiple types of weighted steps combined with neighborhood sequences, were developed. With appropriate weight sequences, the distance between points on the perimeter of a square and the center of the square (i.e., for squares of a given size the weight sequence can be easily computed) are exactly the Euclidean distance for these distances based on weight sequences. However, distances based on weight sequences may not fulfill the triangular inequality. In this paper, continuing the research, we provide a sufficient condition for weight sequences to provide metric distance. Further, we present an algorithm to compute the distance transform based on these distances. Optimization results are also shown for the approximation of the Euclidean distance inside the given square.
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| 2. |
- Normand, Nicolas, et al.
(författare)
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A Streaming Distance Transform Algorithm for Neighborhood-Sequence Distances
- 2014
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Ingår i: Image Processing On Line. - : Image Processing On Line. - 2105-1232. ; 4, s. 196-203
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Tidskriftsartikel (refereegranskat)abstract
- We describe an algorithm that computes a “translated” 2D Neighborhood-Sequence Distance Transform (DT) using a look up table approach. It requires a single raster scan of the input image and produces one line of output for every line of input. The neighborhood sequence is specified either by providing one period of some integer periodic sequence or by providing the rate of appearance of neighborhoods. The full algorithm optionally derives the regular (centered) DT from the “translated” DT, providing the result image on-the-fly, with a minimal delay, before the input image is fully processed. Its efficiency can benefit all applications that use neighborhood- sequence distances, particularly when pipelined processing architectures are involved, or when the size of objects in the source image is limited.
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| 3. |
- Normand, Nicolas, et al.
(författare)
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Digital Distances and Integer Sequences
- 2013
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Ingår i: Lecture Notes in Computer Science. ; , s. 169-179
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Konferensbidrag (refereegranskat)abstract
- In recent years, the theory behind distance functions defined by neighbourhood sequences has been developed in the digital geometry community. A neighbourhood sequence is a sequence of integers, where each element defines a neighbourhood. In this paper, we establish the equivalence between the representation of convex digital disks as an intersection of half-planes ( H -representation) and the expression of the distance as a maximum of non-decreasing functions.Both forms can be deduced one from the other by taking advantage of the Lambek-Moser inverse of integer sequences.Examples with finite sequences, cumulative sequences of periodic sequences and (almost) Beatty sequences are given. In each case, closed-form expressions are given for the distance function and H -representation of disks. The results can be used to compute the pair-wise distance between points in constant time and to find optimal parameters for neighbourhood sequences.
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