Mousumi Dutt

On finding a shortest isothetic path and its monotonicity inside a digital object

Algorithms for finding shortest paths and their numerous variants have been studied extensively over several decades in graph theory, computational geometry, and in operations research. Still, design of such algorithms poses newer challenges in various emerging areas of image analysis and computer vision. This mandates further investigation of application-specific shortest-path problems in the framework of digital geometry. We present here an efficient combinatorial algorithm for finding a shortest isothetic path (SIP) between two grid points in a digital object without any hole, such that the SIP lies entirely inside the object. Our algorithm first determines a maximum-area isothetic polygon that is inscribed within the object. Certain combinatorial rules are then used to construct the SIP on the basis of its constituent monotone sub-paths, the number of which is invariant regardless of the choice of SIP between two given grid points. For a given grid size, the proposed algorithm runs in O(nlogn)

Number of Shortest Paths in Triangular Grid for 1- and 2-Neighborhoods

O(n\log n)

Characterization and generation of straight line segments on triangular cell grid

time, where n is the number of grid points appearing on the boundary of the inscribed polygon. Experimental results show the effectiveness of the algorithm and its further prospects in shape analysis.

Finding a largest rectangle inside a digital object and rectangularization

This paper presents a novel formulation to determine the number of shortest paths between two points in triangular grid in 2D digital space. Three types of neighborhood relations are used on the triangular grid. Here, we present the solution of the above mentioned problem for two neighborhoods--1-neighborhood and 2-neighborhood. To solve the stated problem we need the coordinate triplets of the two points. This problem has theoretical aspects and practical importance.

Finding Shortest Triangular Path in a Digital Object

Abstract In this paper we are considering straight lines and straight line segments defined by two triangle centroids in the triangular cell grid. A generation algorithm determining all the triangles (triangular cells) that are crossed by a straight line segment is proposed. There is the particular case where straight lines or straight line segments cross a vertex of the grid. We propose an arithmetical characterization of such lines and line segments.

Finding Largest Rectangle Inside a Digital Object

Abstract A combinatorial algorithm to find a largest rectangle (LR) inside the inner isothetic cover which tightly inscribes a given digital object without holes is presented here which runs in O ( k . n / g + ( n / g ) log ⁡ ( n / g ) ) time, where n , g , and k being the number of pixels on the contour of the digital object, grid size, and the number of convex regions, respectively. Certain combinatorial rules are formulated to obtain an LR. An LR divides the object in several parts. The object can be rectangularized by recursive generation of a set of LRs and it generates LR-Graph which is useful for shape analysis.

Enumeration of Shortest Isothetic Paths Inside a Digital Object

A combinatorial algorithm to find a shortest triangular path STP between two points inside a digital object imposed on triangular grid is designed having

A Study on the Properties of 3D Digital Straight Line Segments

O\frac{n}{g} \log \frac{n}{g}