| 1. |
- Nagy, Benedek, et al.
(författare)
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Neighborhood Sequences in the Diamond Grid : Algorithms with Two and Three Neighbors
- 2009
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Ingår i: International journal of imaging systems and technology (Print). - : Wiley Periodicals, Inc.. - 0899-9457 .- 1098-1098. - 9783540896456 ; 19:2, s. 146-157
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Tidskriftsartikel (refereegranskat)abstract
- In the digital image processing, digital distances are useful; distances based on neighborhood sequences are widely used. In this article, the diamond grid is considered, that is, the three-dimensional grid of carbon atoms in the diamond crystal. An algorithm to compute a shortest path defined by a neighborhood sequence between any two points in the diamond grid is presented. A formula to compute the distance based on neighborhood sequences with two neighborhood relations is given. The metric and nonmetric properties of some distances based on neighborhood sequences are also discussed. Finally, the constrained distance transformation is shown.
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| 2. |
- Nagy, Benedek, et al.
(författare)
-
Neighborhood Sequences in the Diamond Grid - Algorithms with Four Neighbors
- 2009
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Ingår i: <em>Proceedings, theoretical track, International Workshop on Combinatorial Image Analysis (IWCIA 2009), Mexico</em>. - Berlin / Heidelberg : Springer. - 9783540896456 ; , s. 109-121
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Konferensbidrag (refereegranskat)abstract
- In digital image processing digital distances are useful; distances based on neighborhood sequences are widely used. In this paper the diamond grid is considered, that is the three-dimensional grid of Carbon atoms in the diamond crystal. This grid can be described by four coordinate values using axes of the directions of atomic bonds. In this way the sum of the coordinate values can be either zero or one. An algorithm to compute a shortest path defined by a neighborhood sequence between any two points in the diamond grid is presented. The metric and non-metric properties of some distances based on neighborhood sequences are also discussed. The constrained distance transformation and digital balls obtained by some distance functions are presented.
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| 3. |
- Nagy, Benedek, et al.
(författare)
-
Neighborhood Sequences on nD Hexagonal/Face-Centered-Cubic Grids
- 2009
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Ingår i: <em>Proceedings, theoretical track, International Workshop on Combinatorial Image Analysis (IWCIA 2009), Mexico</em>. - Berlin / Heidelberg : Springer. - 9783540896456 ; , s. 96-108
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Konferensbidrag (refereegranskat)abstract
- The two-dimensional hexagonal grid and the three-dimensional face-centered cubic grid can be described by intersecting Z3 and Z4 with a (hyper)plane. Corresponding grids in higher dimensions (nD) are examined. In this paper, we define distance functions based on neighborhood sequences on these, higher dimensional generalizations of the hexagonal grid. An algorithm to produce a shortest path based on neighborhood sequences between any two gridpoints is presented. A formula to compute distance and condition of metricity are presented for neighborhood sequences using two types of neighbors. Distance transform as an application of these distances is also shown.
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| 4. |
- 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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| 5. |
- Strand, Robin, 1978-
(författare)
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Distance Functions and Image Processing on Point-Lattices : with focus on the 3D face- and body-centered cubic grids
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- There are many imaging techniques that generate three-dimensional volume images today. With higher precision in the image acquisition equipment, storing and processing these images require increasing amount of data processing capacity. Traditionally, three-dimensional images are represented by cubic (or cuboid) picture elements on a cubic grid. The two-dimensional hexagonal grid has some advantages over the traditionally used square grid. For example, less samples are needed to get the same reconstruction quality, it is less rotational dependent, and each picture element has only one type of neighbor which simplifies many algorithms. The corresponding three-dimensional grids are the face-centered cubic (fcc) grid and the body-centered cubic (bcc) grids. In this thesis, image representations using non-standard grids is examined. The focus is on the fcc and bcc grids and tools for processing images on these grids, but distance functions and related algorithms (distance transforms and various representations of objects) are defined in a general framework allowing any point-lattice in any dimension. Formulas for point-to-point distance and conditions for metricity are given in the general case and parameter optimization is presented for the fcc and bcc grids. Some image acquisition and visualization techniques for the fcc and bcc grids are also presented. More theoretical results define distance functions for grids of arbitrary dimensions. Less samples are needed to represent images on non-standard grids. Thus, the huge amount of data generated by for example computerized tomography can be reduced by representating the images on non-standard grids such as the fcc or bcc grids. The thesis gives a tool-box that can be used to acquire, process, and visualize images on high-dimensional, non-standard grids.
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| 6. |
- Strand, Robin, 1978-, et al.
(författare)
-
Path-Based Distance Functions in n-Dimensional Generalizations of the Face- and Body-Centered Cubic Grids
- 2009
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Ingår i: Discrete Applied Mathematics. - : Elsevier. - 0166-218X .- 1872-6771. - 9783540896456 ; 157:16, s. 3386-3400
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Tidskriftsartikel (refereegranskat)abstract
- Path-based distance functions are defined on n-dimensional generalizations of the face-centered cubic and body-centered cubic grids. The distance functions use both weights and neighborhood sequences. These distances share many properties with traditional path-based distance functions, such as the city-block distance, but are less rotational dependent. For the three-dimensional case, we introduce four different error functions which are used to find the optimal weights and neighborhood sequences that can be used to define the distance functions with low rotational dependency.
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| 7. |
- Strand, Robin, 1978-, et al.
(författare)
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The Polar Distance Transform by Fast-Marching
- 2008
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Ingår i: Proceedings of 19th International Conference on Pattern Recognition (ICPR 2008), Tampa, Florida, December 2008. - : IEEE computer society. - 9781424421756
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Konferensbidrag (refereegranskat)abstract
- Image analysis tools that process the image using polar coordinates are needed to avoid the interpolation from polar to cartesian coordinates. We present a tool for analysing and processing circular objects – the polar distance transform computed by fast-marching. The fast marching method can be used for computing the grey-weighted distance transform by numerically approximating the Eikonal differential equation. We modify the Eikonal equation using weights that depend on the radius and angle relative to a pre-defined coordinate system.
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| 8. |
- Strand, Robin, 1978-
(författare)
-
Weighted Distances Based on Neighborhood Sequences for Point-Lattices
- 2009
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Ingår i: Discrete Applied Mathematics. - : Elsevier. - 0166-218X .- 1872-6771. - 9783540896456 ; 157:4, s. 641-652
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Tidskriftsartikel (refereegranskat)abstract
- A path-based distance is defined as the minimal cost-path between two points. One such distance function is the weighted distance based on a neighborhood sequence. It can be defined using any number of neighborhood relations and weights in conjunction with a neighborhood sequence. The neighborhood sequence restricts some steps in the path to a smaller neighborhood. We give formulas for computing the point-to-point distance and conditions for metricity for weighted distances based on neighborhood sequences with two neighborhood relations for the general case of point-lattices.
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