Partha Pratim Das

Distance functions in digital geometry

Abstract An analysis of paths and distances in n dimensions is carried out using variable neighborhood sequences. A symbolic expression for the distance function between any two points in this quantized space is derived. An algorithm for finding the shortest path is presented. The necessary and sufficient condition for such distance functions to satisfy the properties of a metric has been derived. Certain practical and efficient methods to check for metric properties are also presented.

Knight's distance in digital geometry

Abstract Using the knights moves in the game of chess, the knights distance is defined for the digital plane. Its functional form is presented. An algorithm is given for tracing a minimal knights path. The properties of some related topological entities are explored. Finally, the knights transform is defined.

Generalized distances in digital geometry

A generalized distance measure called m-neighbor distance in n-D quantized space is presented. Its properties as a metric are examined. It is shown to give the shortest path length between two points in n-D digital space. An algorithm for finding such a shortest path between two points is presented. It is shown that lower dimension (2-D and 3-D) distance measures presently used in digital geometry can easily be derived as special cases. Other properties of m-neighbor distance are also examined.

Characterizations of Noise in Kinect Depth Images: A Review

In this paper, we characterize the noise in Kinect depth images based on multiple factors and introduce a uniform nomenclature for the types of noise. In the process, we briefly survey the noise models of Kinect and relate these to the factors of characterization. We also deal with the noise in multi-Kinect set-ups and summarize the techniques for the minimization of interference noise. Studies on noise in Kinect depth images are distributed over several publications and there is no comprehensive treatise on it. This paper, to the best of our knowledge, is the maiden attempt to characterize the noise behavior of Kinect depth images in a structured manner. The characterization would help to selectively eliminate noise from depth images either by filtering or by adopting appropriate methodologies for image capture. In addition to the characterization based on the results reported by others, we also conduct independent experiments in a number of cases to fill up the gaps in characterization and to validate the reported results.

Lattice of octagonal distances in digital geometry

Abstract In this paper we identify a natural ordering relation R between octagonnal distances ( d ( B )), defined by neighbourhood sequences ( B ) in two-dimensional digital geometry. We prove that R induces a complete compact distributive lattice over the set of B s (and hence the set of d ( B )s) in 2-D.

Octagonal distances for digital pictures

Abstract The set of distances obtained by combining the cityblock and the chessboard motions is studied as a generalization of the octagonal distance for digital pictures. The corresponding digital disks are shown to be digital octagons. A necessary and sufficient condition is obtained for the triangularity of these distances. The suitability of these distances as approximations of the Euclidean distance is studied using three different indices of errors.

Metricity of super-knight's distance in digital geometry

Abstract In this paper we have extended the knights moves in chess to introduce super-knights moves in digital geometry. They define super-knights distance (like the knights distance [1]). However, all super-knights distances are not metrics. We have proved a theorem to show that a super-knights distance is a metric if and only if the underlying super-knights move is well-behaved in a specific sense. We conclude with suggestions on future study.

On connectivity issues of ESPTA

Abstract In this paper we review the connectivity properties of our 3-D thinning algorithm ESPTA (Extended Safe Point Thinning Algorithm [2]) and its other versions. We present a modification of ESPTA, called MESPTA, which preserves the connectivity of the image while maintaining its 3-D shape.

On approximating Euclidean metrics by digital distances in 2D and 3D

Abstract In this paper a geometric approach is suggested to find the closest approximation to Euclidean metric based on geometric measures of the digital circles in 2D and the digital spheres in 3D for the generalized octagonal distances. First we show that the vertices of the digital circles (spheres) for octagonal distances can be suitably approximated as a function of the number of neighborhood types used in the sequence. Then we use these approximate vertex formulae to compute the geometric features in an approximate way. Finally we minimize the errors of these measurements with respect to respective Euclidean discs to identify the best distances. We have verified our results by experimenting with analytical error measures suggested earlier. We have also compared the performances of the good octagonal distances with good weighted distances. It has been found that the best octagonal distance in 2D ({1,1,2}) performs equally good with respect to the best one for the weighted distances (〈3,4〉). In fact in 3D, the octagonal distance {1,1,3} has an edge over the other good weighted distances.

Thinning of 3-D images using the Safe Point Thinning Algorithm (SPTA)

Abstract In this paper the Extended Safe Point Thinning Algorithm (ESPTA) is presented for thinning 3-D images. It is developed on a 2-D algorithm by Naccache & Shinghal (1984). It is shown that ESPTA preserves the 18-connectivity of the image. Some experimental results with ESPTA will also be discussed.