Muthuganapathy Ramanathan

Given a planar point set sampled from a curve, the curve reconstruction problem computes a polygonal approximation of the curve. In this paper, we propose a Delaunay triangulation-based algorithm for curve reconstruction, which removes the longest edge of each triangle to result in a graph. Further, each vertex of the graph is checked for a degree constraint to compute simple closed/open curves. Assuming ϵ-sampling, we provide theoretical guarantee which ensures that a simple closed/open curve is a piecewise linear approximation of the original curve. Input point sets with outliers are handled as part of the algorithm, without pre-processing. We also propose strategies to identify the presence of noise and simplify a noisy point set, identify self-intersections and enhance our algorithm to reconstruct such point sets. Perhaps, this is the first algorithm to identify the presence of noise in a point set. Our algorithm is able to detect closed/open curves, disconnected components, multiple holes and sharp corners. The algorithm is simple to implement, independent of the type of input, non-feature specific and hence it is a generalized one. We have performed extensive comparative studies to demonstrate that our method is comparable or better than other existing methods. Limitations of our approach have also been discussed.

Epileptic seizures are characterized by the excessive and abrupt electrical discharge in the brain. This asynchronous firing of neurons causes unprovoked convulsions which can be a cause of sudden unexpected death in epilepsy (SUDEP). Remote monitoring of epileptic patients can help prevent SUDEP. Systems based on wearable accelerometer sensors have shown to be effective in ambulatory monitoring of epileptic patients. However, these systems have a trade-off between seizure duration and the false alarm rate (FAR). The FAR of the system decreases as we increase the seizure duration. Further, multiple sensors are used in conjugation to improve the overall performance of the detection system. In this study, we propose a system based on single wrist-worn accelerometer sensor capable of detecting seizures with short duration (≥ 10s). Seizure detection was performed by employing machine learning approach such as kernelized support vector data description (SVDD). The proposed approach is validated on data collected from 12 patients, corresponding to approximately 966h of recording under video-telemetry unit. The algorithm resulted in a seizure detection sensitivity of 95.23% with a mean FAR of 0.72=24h.

In this paper, we propose a Delaunay triangulation based algorithmic framework for the 2D point set type discernment and its reconstruction. The point set discernment deals with determining whether the given point set S consists of only the points sampled along the boundary of an object (referred to as boundary sample) or S is distributed across the object (referred to as dot-pattern). In general, the existing approaches deal with the reconstruction of an a priori known input type - boundary sample or dot-pattern. Our approach works on both sets of input data type by first identifying the input type that a given point set belongs to. To distinguish the point set type, we introduce the notion of Petal-Ratio(PR) which captures the ratio of the longest edge to the smallest edge emanating from a vertex in Delaunay triangulation. Further, we employ the Petal-Ratio as the essence to design simple reconstruction algorithms pertaining to each input type that unveil the shape of the object hidden in the given point set. The reconstruction algorithms start with computing the Delaunay triangulation of the given point set and for each vertex, the Petal-Ratio is calculated. Following this, the edges are removed based on the value of the PR for every vertex to arrive at the boundaries. Theoretical analysis of determining appropriate values of PRs under ϵ- sampling and minimal reach sampling models have been presented. Unlike many other algorithms, our approach is non-parametric and non-feature specific that can capture features like disconnected components, multiple holes even with the presence of outliers, self-intersection (only for boundary sample) and open curves (only for boundary sample). Moreover, our algorithms take only one pass to reconstruct the hole boundaries as well as outer boundary irrespective of the object features like the number of holes and the number of components. The comparative analysis shows that our algorithms perform equally well or better than their counterparts for the objects with contrasting features. We also demonstrate that the proposed idea can be easily extended to surface reconstruction.

Visual inspection system of various manufactured geometries is widely adopted in industry whereas the inspection system's intelligence is yet to be improved. Mixing of various geometries is a common problem in coating industry and the inspection is carried out manually. This paper gives a framework for classifying the mixed parts from the images captured without prior information of geometries. The parts were segmented from the image using Otsu method followed by morphological operations. Then the borders were extracted and smoothened by Fourier approximation. The touching objects were separated using curvature analysis. Features such as area and skeleton were extracted from the individual parts. The geometries were then classified by k-means clustering successfully. The developed algorithm works for a variety of geometries and is independent of translation and rotation of the parts. © 2013 © 2013 CAD Solutions, LLC.

We propose an algorithm to compute and maintain the spatial proximities of planar points continuously moving along predefined linear trajectories. The proximity information of moving points is captured and maintained via the well known Gabriel graph adapted for the kinetic setting, called kinetic Gabriel graph (KGG). Kinetic Gabriel Graph is built on top of the kinetic framework of Delaunay graph. Leveraging the positioning of the Delaunay circumcenters relative to the corresponding Delaunay triangles, we formulate `Gabriel certificates' that determine whether or not an edge of a Delaunay triangle is Gabriel. Then we employ an edge tagging algorithm to maintain the set of all Gabriel edges from the Delaunay graph as the points move. The proposed algorithm has been evaluated using numerous test data, and various computational implications with respect to the topological events occurring in the data structure during the points' movement have been discussed. We also provide a conceptual demonstration of the practical potentials of the proposed algorithm in video based monitoring systems.

We present a drawing assistant for sketching and for assisting users in shading a hand drawn sketch. The augmented reality based system uses a sketch made by a professional and uses it to help inexperienced users to do sketching and shading. The input image is converted to a set of points based on simple heuristics for providing a "connect the dots" interface for a user to aid sketching. With the help of a 2.5D mesh generated by our algorithm, the system assists the user by providing information about the colors that can be given in different parts of the sketch. The system was tested with users of different age groups and skill levels, indicating its usefulness.

ABSTRACT: We present a method to extract the contour of geometric objects embedded in binary digital images using techniques in computational geometry. Rather than directly dealing with pixels as in traditional contour extraction methods, we process on object point set extracted from the image. The proposed algorithm works in four phases: point extraction, Euclidean graph construction, point linking and contour simplification. In point extraction phase, all pixels that represent the object pattern are extracted as a point set from the input image. We use the color segmentation to distinguish the object pixels from the background pixels. In the second phase, a geometric graph G=(V,E) is constructed, where V consists of the extracted object point set and E consists of all possible edges whose Euclidean distance is less than a threshold parameter, l ; which can be derived from the available information from the point set. In point linking phase, all border points are connected to generate the contour using the orientation information inferred from the clockwise turn angle at each border point. Finally, the extracted contour is simplified using collinearity check. Experiments on various standard binary images show that the algorithm is capable of constructing contours with high accuracy and achieves high compression ratio in noisy and non-noisy binary images.

Computing the shortest path, overcoming obstacles in a plane, is a well-known geometric problem. However, widely assumed obstacles are polygonal in nature. Very few papers have focused on curved obstacles, and in particular, for curved multiply-connected domains (domains having holes). Given a set of parametric curves forming a multiply-connected domain (MCD), with one closed curve acting as an outer boundary and several non-intersecting inner curves (loops) as representing holes and two distinct points S and E lying on the outer boundary, this paper provides an algorithm to find the shortest interior path (SIP) between the two points in the domain. SIP consists of portions of curves along with straight line segments that are tangential to the curve. The algorithm initially computes point-curve tangents (PCTs) and bitangents (BTs) using their respective constraints. A generalized region lemma is proposed, which is then employed to remove PCTs/BTs that will not contribute to the potential path and subsequently aiding in removing a few inner loops. The algorithm is designed to explore all potential paths. Merging of paths is also proposed to avoid redundant computations. A final SIP is chosen from potential paths using the length of each path. The algorithm also has the potential to give all paths of equal lengths contributing to shortest paths (within a tolerance level). As the algorithm computes all the potential paths on the fly, there is no need to employ a visibility graph to compute the shortest path. Curves are represented using non-uniform rational B-splines (NURBS). The algorithm uses the curves as such and does not discretize into point-sets or polygons. Extensions to handle curves with C1 discontinuities and S and E not on the outer boundary have also been described. Results of the implementation are provided and complexity of the algorithm is also discussed. This paper follows up the one presented for simply-connected domains (SCDs) in Bharath Ram and Ramanathan (2011) [4]. © 2012 Elsevier Ltd. All rights reserved.

We present a mixed reality-based assistive system for shading paper sketches. Given a paper sketch made by an artist, our interface helps inexperienced users to shade it appropriately. Initially, using a simple Delaunay-triangulation based inflation algorithm, an approximate depth map is computed. The system then highlights areas (to assist shading) based on a rendering of the 2.5-dimensional inflated model of the input contour. With the help of a mixed reality system, we project the highlighted areas back to aid users. The hints given by the system are used for shading and are smudged appropriately to apply an artistic shading to the sketch. The user is given flexibility at various levels to simulate conditions such as height and light position. Experiments show that the proposed system aids novice users in creating sketches with impressive shading.