Department of Computer Science & Engineering

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IIT Jodhpur

Globally, cataract is a common eye disease and one of the leading causes of blindness and vision impairment. The traditional process of detecting cataracts involves eye examination using a slit-lamp microscope or ophthalmoscope by an ophthalmologist, who checks for clouding of the normally clear lens of the eye. The lack of resources and unavailability of a sufficient number of experts pose a burden to the healthcare system throughout the world and researchers are exploring the use of AI solutions for assisting the experts. Inspired by the progress in iris recognition, in this research, we present a novel algorithm for cataract detection using near-infrared eye images. The NIR cameras, which are popularly used in iris recognition, are of relatively low cost and easy to operate compared to ophthalmoscope setup for data capture. However, such NIR images have not been explored for cataract detection. We present deep learning-based eye segmentation and multitask network classification networks for cataract detection using NIR images as input. The proposed segmentation algorithm efficiently and effectively detects non-ideal eye boundaries and is cost-effective and the classification network yields very high classification performance on the cataract dataset.

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Computer Vision and Image Understanding

MTCD: Cataract detection via near infrared eye images

Planar graphs can be represented as intersection graphs of different types of geometric objects in the plane, e.g., circles (Koebe, 1936), line segments (Chalopin & Gonçalves, SODA 2009), L-shapes (Gonçalves et al., SODA 2018). For general graphs, however, even deciding whether such representations exist is often NP -hard. We consider apex graphs, i.e., graphs that can be made planar by removing one vertex from them. We show, somewhat surprisingly, that deciding whether geometric representations exist for apex graphs is NP -hard. More precisely, we show that for every positive integer g, recognizing every graph class G such that PURE-2-DIR⊆G⊆1-STRING is NP -hard, even if the inputs are apex graphs of girth at least g. Here, PURE-2-DIR is the class of intersection graphs of axis-parallel line segments (where intersections are allowed only between horizontal and vertical segments), and 1-STRING is the class of intersection graphs of simple curves (where two curves cross at most once) in the plane. This partially answers an open question raised by Kratochvíl & Pergel (COCOON, 2007). Most known NP -hardness reductions for these problems are from variants of 3-SAT. We reduce from the Planar Hamiltonian Path Completion problem, which uses the more intuitive notion of planarity. As a result, our proof is much simpler and encapsulates several classes of geometric graphs. © 2022, Springer Nature Switzerland AG.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Finding Geometric Representations of Apex Graphs is NP-Hard

We present a novel self-supervised framework for learning the discretization-agnostic surface parameterization of arbitrary 3D objects with both bounded and unbounded surfaces. Our framework leverages diffusion-enabled global-to-local shape context for each vertex first to partition the unbounded surface into multiple patches using the proposed self-supervised PatchNet and subsequently perform independent UV parameterization of these patches by learning forward and backward UV mapping for individual patches. Thus, our framework enables learning a discretization-agnostic parameterization at a lower resolution and then directly inferring the parameterization for a higher-resolution mesh without retraining. We evaluate our framework on multiple 3D objects from the publicly available SHREC [Lian et al. 2011] dataset and report superior/faster UV parameterization over conventional methods. © 2022 ACM.

Proceedings - SIGGRAPH Asia 2022: Technical Communications

Discretization-Agnostic Deep Self-Supervised 3D Surface Parameterization

A digraph D is singly connected if for all ordered pairs of vertices u,v∈V(D), there is at most one path in D from u to v. In this paper, we study the SINGLY CONNECTED VERTEX DELETION (SCVD) problem: Given an n-vertex digraph D and a positive integer k, does there exist a set S⊆V(D) such that |S|≤k and D−S is singly connected? This problem may be seen as a directed counterpart of the (UNDIRECTED) FEEDBACK VERTEX SET problem, as an undirected graph is singly connected if and only if it is acyclic. SCVD is known to be NP-hard on general digraphs. We study the complexity of SCVD on various classes of digraphs such as tournaments, and various generalisations of tournaments such as digraphs of bounded independence number, in- and out-tournaments and local tournaments. We show that unlike the FEEDBACK VERTEX SET ON TOURNAMENTS (FVST) problem, SCVD is polynomial-time solvable on tournaments. In addition, we show that SCVD is polynomial-time solvable on digraphs of bounded independence number, and on the class of acyclic local tournaments. We also study the parameterized complexity of SCVD, with k as the parameter, on the class of in-tournaments. And we show that on in-tournaments, SCVD admits a fixed-parameter tractable algorithm and a quadratic vertex kernel. We also show that on the class of local tournaments, which is a sub-class of in-tournaments, SCVD admits a linear vertex kernel. © 2022 Elsevier B.V.

Theoretical Computer Science

On the complexity of singly connected vertex deletion

Attaining Class-Level Forgetting in Pretrained Model Using Few Samples

2021 16th IEEE International Conference on Automatic Face and Gesture {\ldots}

Dual Sensor Indian Masked Face Dataset

RGB-D Face Recognition using Reconstruction based Shared Representation

When Sketch Face Recognition Meets Mask Obfuscation: Database and Benchmark

In a permutation graph, vertices represent the elements of a permutation, and edges represent pairs of elements that are reversed by the permutation. In the Permutation Vertex Deletion problem, given an undirected graph G and an integer k, the objective is to test whether there exists a vertex subset S⊆ V(G) such that | S| ≤ k and G- S is a permutation graph. The parameterized complexity of Permutation Vertex Deletion is a well-known open problem. Bożyk et al. [IPEC 2020] initiated a study on this problem by requiring that G- S be a bipartite permutation graph (a permutation graph that is bipartite). They called this the Bipartite Permutation Vertex Deletion (BPVD) problem. They showed that the problem admits a factor 9-approximation algorithm as well as a fixed parameter tractable (FPT) algorithm running in time O(9 k| V(G) | 9). Moreover, they posed the question whetherBPVD admits a polynomial kernel. We resolve this question in the affirmative by designing a polynomial kernel for BPVD. In particular, we obtain the following: Given an instance (G, k) of BPVD, in polynomial time we obtain an equivalent instance (G′, k′) of BPVD such that k′≤ k, and | V(G′) | + | E(G′) | ≤ kO(1). © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Algorithmica

A Polynomial Kernel for Bipartite Permutation Vertex Deletion

In the literature on parameterized graph problems, there has been an increased effort in recent years aimed at exploring novel notions of graph edit-distance that are more powerful than the size of a modulator to a specific graph class. In this line of research, Bulian and Dawar [Algorithmica, 75 (2016), pp. 363-382] introduced the notion of elimination distance and showed that deciding whether a given graph has elimination distance at most k to any minor-closed class of graphs is fixed-parameter tractable parameterized by k [Algorithmica, 79 (2017), pp. 139-158]. They showed that graph isomorphism parameterized by the elimination distance to bounded degree graphs is fixed-parameter tractable and asked whether determining the elimination distance to the class of bounded degree graphs is fixed-parameter tractable. Recently, Lindermayr, Siebertz, and Vigny [MFCS 2020, LIPIcs Leibniz Int. Proc. Inform. 170, Wadern Germany, 2020, 65] obtained a fixed-parameter algorithm for this problem in the special case where the input is restricted to K5-minor free graphs. In this paper, we answer the question of Bulian and Dawar in the affirmative for general graphs. In fact, we give a more general result capturing elimination distance to any graph class characterized by a finite set of graphs as forbidden induced subgraphs. © 2022 Society for Industrial and Applied Mathematics