| 1. |
- Strand, Robin, 1978-, et al.
(författare)
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A Connection Between Zn and Generalized Triangular Grids
- 2008
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Ingår i: International Symposium on Visual Computing (ISVC 2008), Las Vegas, Nevada. - Berlin / Heidelberg : Springer. - 9783540896456 ; , s. 1157-1166
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Konferensbidrag (refereegranskat)abstract
- In this paper we show how non-standard three-dimensional grids, such as the face-centered cubic (fcc), the body-centered cubic (bcc), and the diamond grids can be embedded in ℤ4. The fcc grid is a hyperplane in ℤ4, the diamond grid is the union of two parallel hyperplanes. The union of four hyperplanes (in a circular way) gives the bcc grid. Based on these connections, several types of neighborhood structures are introduced on these grids. These structures span from the most natural ones (crystal bonds, Voronoi neighbors) to infinite families.
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| 2. |
- Malmberg, Filip, 1980-, et al.
(författare)
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When Can lp-norm Objective Functions Be Minimized via Graph Cuts?
- 2018
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Ingår i: Combinatorial Image Analysis. - Cham : Springer. - 9783030052874 ; , s. 112-117
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Konferensbidrag (refereegranskat)abstract
- Techniques based on minimal graph cuts have become a standard tool for solving combinatorial optimization problems arising in image processing and computer vision applications. These techniques can be used to minimize objective functions written as the sum of a set of unary and pairwise terms, provided that the objective function is sub-modular. This can be interpreted as minimizing the l1-norm of the vector containing all pairwise and unary terms. By raising each term to a power p, the same technique can also be used to minimize the lp-norm of the vector. Unfortunately, the submodularity of an l1-norm objective function does not guarantee the submodularity of the corresponding lp-norm objective function. The contribution of this paper is to provide useful conditions under which an lp-norm objective function is submodular for all p>= 1, thereby identifying a large class of lp-norm objective functions that can be minimized via minimal graph cuts.Techniques based on minimal graph cuts have become a standard tool for solving combinatorial optimization problems arising in image processing and computer vision applications. These techniques can be used to minimize objective functions written as the sum of a set of unary and pairwise terms, provided that the objective function is submodular. This can be interpreted as minimizing the l1l1-norm of the vector containing all pairwise and unary terms. By raising each term to a power p, the same technique can also be used to minimize the lplp-norm of the vector. Unfortunately, the submodularity of an l1l1-norm objective function does not guarantee the submodularity of the corresponding lplp-norm objective function. The contribution of this paper is to provide useful conditions under which an lplp-norm objective function is submodular for all p≥1p≥1, thereby identifying a large class of lplp-norm objective functions that can be minimized via minimal graph cuts.
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| 3. |
- Strand, Robin, 1978-, et al.
(författare)
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The Minimum Barrier Distance : A Summary of Recent Advances
- 2017
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Ingår i: Discrete Geometry for Computer Imagery. DGCI 2017. - Cham : Springer. - 9783319662725 - 9783319662718 ; , s. 57-68
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Konferensbidrag (refereegranskat)abstract
- In this paper we present an overview and summary of recent results of the minimum barrier distance (MBD), a distance operator that is a promising tool in several image processing applications. The theory constitutes of the continuous MBD in Rn, its discrete formulation in Zn (in two different natural formulations), and of the discussion of convergence of discrete MBDs to their continuous counterpart. We describe two algorithms that compute MBD, one very fast but returning only approximate MBD, the other a bit slower, but returning the exact MBD. Finally, some image processing applications of MBD are presented and the directions of potential future research in this area are indicated.
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| 4. |
- Linner, Elisabeth, et al.
(författare)
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Comparison of Restoration Quality on Square and Hexagonal Grids using Normalized Convolution
- 2012
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Ingår i: Proceedings of the 21st International Conference on Pattern Recognition (ICPR).
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Konferensbidrag (refereegranskat)abstract
- Normalized convolution can be used to restore information that has been lost from an image, such as dead pixels, using the remaining information, and ignoring the incorrect pixels. It is known that the representation quality of an image consisting of a given number of pixels depends on how these pixels are distributed. In this paper, we investigate whether the ability to restore information using normalized convolution is affected by the sampling grid of the image. We compare square and hexagonal grids, and find that, in general, more pixels can be restored in hexagonal grids.
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| 5. |
- 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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| 6. |
- 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 .- 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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| 7. |
- 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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| 8. |
- Strand, Robin, 1978-
(författare)
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Minimal paths by sum of distance transforms
- 2016
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Ingår i: Discrete Geometry for Computer Imagery. - Cham : Springer. - 9783319323596 ; , s. 349-358
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Konferensbidrag (refereegranskat)
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| 9. |
- Strand, Robin, 1978-, et al.
(författare)
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The Minimum Barrier Distance - Stability to seed point position
- 2014
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Ingår i: Discrete Geometry for Computer Imagery, DGCI 2014. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 9783319099545 - 9783319099552 ; , s. 111-121
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Konferensbidrag (refereegranskat)abstract
- Distance and path-cost functions have been used for image segmentation at various forms, e.g., region growing or live-wire boundary tracing using interactive user input. Different approaches are associated with different fundamental advantages as well as difficulties. In this paper, we investigate the stability of segmentation with respect to perturbations in seed point position for a recently introduced pseudo-distance method referred to as the minimum barrier distance. Conditions are sought for which segmentation results are invariant with respect to the position of seed points and a proof of their correctness is presented. A notion of δ-interface is introduced defining the object-background interface at various gradations and its relation to stability of segmentation is examined. Finally, experimental results are presented examining different aspects of stability of segmentation results to seed point position.
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