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A Measure of Directional Convexity Inspired by Binary Tomography

Balázs P., Ozsvár Z., Tasi T. S., Nyúl L. G.

Fundamenta Informaticae

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2015

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Vol. 141, nr 2/3

151--167

EN

Inspired by binary tomography, we present a measure of directional convexity of binary images combining various properties of the configuration of 0s and 1s in the binary image. The measure can be supported by proper theory, is easy to compute, and as shown in our experiments, behaves intuitively. The measure can be useful in numerous applications of digital image processing and pattern recognition, and especially in binary tomography. We show in detail an application of this latter one, by providing a novel reconstruction algorithm for almost hv-convex binary images. We also present experimental results and mention some of the possible generalizations of the measure.

2

A Fast and Automated Granulometric Image Analysis Based on Digital Geometry

Bera S., Biswas A., Bhattacharya B. B.

Fundamenta Informaticae

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2015

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Vol. 138, nr 3

321--338

EN

Granular object segmentation is an important area of image processing, which has several practical applications in agriculture, food industry, geology, and forensics. In this paper, we present a simple algorithm for the analysis of granulometric images that consist of touching or overlapping convex objects such as coffee bean, food grain, nuts, blood cell, or cookies. The algorithm is based on certain underlying digital-geometric features embedded in their binary snapshots. The concept of an outer isothetic cover and the property of geometric convexity are used to extract the joining points (or concavity points) from the ensemble of objects. Next, a combinatorial technique is employed to determine the separator of two overlapping or neighboring objects. This technique is fully automated and it needs only integer-domain computation. The termination time of the algorithm can be tradedoff with the quality of segmentation by changing the resolution parameter. Experimental results for a variety of objects chosen from different application domains such as cell image, coffee-bean image and others demonstrate the efficiency and robustness of the proposed method compared to earlier watershed-based algorithms.

3

Real Polygonal Covers of Digital Discs - Some Theories and Experiments

Bhowmick P., Bhattacharya Bhargab.B.

Fundamenta Informaticae

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2009

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Vol. 91, nr 3-4

487-505

EN

There are several algorithms for digitization of a real disc (circle) to derive a digital disc, and also for finding the real disc corresponding to a digital disc. However, the correspondence of a digital disc with a regular polygon in the real plane is not well studied. This paper presents some theories and related experiments on setting the correspondence from a digital disc to its polygonal cover in the real plane. For an ideal regular polygon covering a digital disc, all the grid points of the digital disc should lie on and inside the polygon, and vice versa. That an ideal regular polygon corresponding to a digital disc is possible for some of the digital discs, especially for the ones having smaller radii, is shown. Further, for a disc whose ideal regular polygon is not possible, an approximate polygon, tending to the ideal one, is possible, in which the error of approximation can be controlled by the number of vertices of the approximate polygon. These (ideal or approximate) polygonal covers of digital discs have several applications in many problems of point set pattern matching. We have reported the conditions under which an ideal regular polygon always exists corresponding to a digital disc, and the conditions under which the existence of an ideal regular polygon becomes uncertain. Experimental results have been given to demonstrate the possibilities of approximation and the trade-off in terms of error versus the number of vertices in the approximate polygon.

4

The length of digital curves

Klette R., Yip B.

Machine Graphics and Vision

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2000

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Vol. 9, No. 3

673-703

EN

The aper discusses one of the elementary subjects in image analysis: how to measure the lenght of a digital curve. A digital curve in the plane is defined to be a cycle given either as an alternating sequence of vertices and edges, or an alternating sequence of edges and squares. The paper reports about two lenght estimators, one based on the partition of a frontier of a simply-connected isothetic polygon into digital straight segments, and one based on calculating the minimum-lenght polygon within an open boundary of a simply-connected isothetic polygon. Both techniques are known to be implementations of covergent estimators of the perimeter of bounded, polygonal or smooth convex sets in the euclidean plane. For each technique a linear-time algorithm is specified, and both algorithms are compared with respect to convergence speed and number of generated segments. The experiments show convergent behavior also for perimeters of non-convex bounded subsets of the euclidean plane.