Rajendra Nagar

Bio: Rajendra Nagar is an academic researcher from Indian Institute of Technology Gandhinagar. The author has contributed to research in topics: Reflection symmetry & Symmetry (geometry). The author has an hindex of 6, co-authored 18 publications receiving 80 citations. Previous affiliations of Rajendra Nagar include Indian Institute of Technology, Jodhpur.

Detecting Approximate Reflection Symmetry in a Point Set Using Optimization on Manifold

Abstract: We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb {R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting approximate reflection symmetry as the problem of establishing correspondences between the points which are reflections of each other and we determine the reflection symmetry transformation. We formulate an optimization framework in which the problem of establishing the correspondences amounts to solving a linear assignment problem and the problem of determining the reflection symmetry transformation amounts to solving an optimization problem on a smooth Riemannian product manifold. The proposed approach estimates the symmetry from the geometry of the points and is descriptor independent. We evaluate the performance of the proposed approach on the standard benchmark dataset and achieve the state-of-the-art performance. We further show the robustness of our approach by varying the amount of distortion in a perfect reflection symmetry pattern where we perturb each point by a different amount of perturbation. We demonstrate the effectiveness of the method by applying it to the problem of 2-D (two-dimensional) and 3-D reflection symmetry detection along with comparisons.

Fast and Accurate Intrinsic Symmetry Detection

Abstract: In computer vision and graphics, various types of symmetries are extensively studied since symmetry present in objects is a fundamental cue for understanding the shape and the structure of objects. In this work, we detect the intrinsic reflective symmetry in triangle meshes where we have to find the intrinsically symmetric point for each point of the shape. We establish correspondences between functions defined on the shapes by extending the functional map framework and then recover the point-to-point correspondences. Previous approaches using the functional map for this task find the functional correspondences matrix by solving a non-linear optimization problem which makes them slow. In this work, we propose a closed form solution for this matrix which makes our approach faster. We find the closed-form solution based on our following results. If the given shape is intrinsically symmetric, then the shortest length geodesic between two intrinsically symmetric points is also intrinsically symmetric. If an eigenfunction of the Laplace-Beltrami operator for the given shape is an even (odd) function, then its restriction on the shortest length geodesic between two intrinsically symmetric points is also an even (odd) function. The sign of a low-frequency eigenfunction is the same on the neighboring points. Our method is invariant to the ordering of the eigenfunctions and has the least time complexity. We achieve the best performance on the SCAPE dataset and comparable performance with the state-of-the-art methods on the TOSCA dataset.

Reflection Symmetry Axes Detection Using Multiple Model Fitting

Abstract: We propose an energy minimization approach to detect multiple reflection symmetry axes present in a given image representing fronto-parallel view of a scene. We perform local feature matching to detect the pairs of mirror symmetric points, and in order to formulate an energy function, we use the geometric characteristics of the symmetry axis. That is, it passes through the midpoint of line segment joining the two mirror symmetric points and is perpendicular to the vector joining two mirror symmetric points. We propose a novel $k$ - symmetry clustering algorithm to minimize this energy function in order to efficiently find all the symmetry axes present in the given image. We evaluate the proposed method on the standard datasets and show that we get comparable and better results than that of the state-of-the-art reflection symmetry detection methods.

ZoomOut: spectral upsampling for efficient shape correspondence

Abstract: We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis. We show how this approach can be used in conjunction with existing initialization techniques across a range of application scenarios, including symmetry detection, map refinement across complete shapes, non-rigid partial shape matching and function transfer. In each application we demonstrate an improvement with respect to both the quality of the results and the computational speed compared to the best competing methods, with up to two orders of magnitude speed-up in some applications. We also demonstrate that our method is both robust to noisy input and is scalable with respect to shape complexity. Finally, we present a theoretical justification for our approach, shedding light on structural properties of functional maps.

ZoomOut: Spectral Upsampling for Efficient Shape Correspondence

Abstract: We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis. We show how this approach can be used in conjunction with existing initialization techniques across a range of application scenarios, including symmetry detection, map refinement across complete shapes, non-rigid partial shape matching and function transfer. In each application we demonstrate an improvement with respect to both the quality of the results and the computational speed compared to the best competing methods, with up to two orders of magnitude speed-up in some applications. We also demonstrate that our method is both robust to noisy input and is scalable with respect to shape complexity. Finally, we present a theoretical justification for our approach, shedding light on structural properties of functional maps.

2017 ICCV Challenge: Detecting Symmetry in the Wild

Abstract: Motivated by various new applications of computational symmetry in computer vision and in an effort to advance machine perception of symmetry in the wild, we organize the third international symmetry detection challenge at ICCV 2017, after the CVPR 2011/2013 symmetry detection competitions. Our goal is to gauge the progress in computational symmetry with continuous benchmarking of both new algorithms and datasets, as well as more polished validation methodology. Different from previous years, this time we expand our training/testing data sets to include 3D data, and establish the most comprehensive and largest annotated datasets for symmetry detection to date; we also expand the types of symmetries to include densely-distributed and medial-axis-like symmetries; furthermore, we establish a challenge-and-paper dual track mechanism where both algorithms and articles on symmetry-related research are solicited. In this report, we provide a detailed summary of our evaluation methodology for each type of symmetry detection algorithm validated. We demonstrate and analyze quantified detection results in terms of precision-recall curves and F-measures for all algorithms evaluated. We also offer a short survey of the paper-track submissions accepted for our 2017 symmetry challenge.

Deep Ensemble Learning for Human Action Recognition in Still Images

Abstract: Numerous human actions such as “Phoning,” “PlayingGuitar,” and “RidingHorse” can be inferred by static cue-based approaches even if their motions in video are available considering one single still image may already sufficiently explain a particular action. In this research, we investigate human action recognition in still images and utilize deep ensemble learning to automatically decompose the body pose and perceive its background information. Firstly, we construct an end-to-end NCNN-based model by attaching the nonsequential convolutional neural network (NCNN) module to the top of the pretrained model. The nonsequential network topology of NCNN can separately learn the spatial- and channel-wise features with parallel branches, which helps improve the model performance. Subsequently, in order to further exploit the advantage of the nonsequential topology, we propose an end-to-end deep ensemble learning based on the weight optimization (DELWO) model. It contributes to fusing the deep information derived from multiple models automatically from the data. Finally, we design the deep ensemble learning based on voting strategy (DELVS) model to pool together multiple deep models with weighted coefficients to obtain a better prediction. More importantly, the model complexity can be reduced by lessening the number of trainable parameters, thereby effectively mitigating overfitting issues of the model in small datasets to some extent. We conduct experiments in Li’s action dataset, uncropped and 1.5x cropped Willow action datasets, and the results have validated the effectiveness and robustness of our proposed models in terms of mitigating overfitting issues in small datasets. Finally, we open source our code for the model in GitHub ( https://github.com/yxchspring/deep_ensemble_learning ) in order to share our model with the community.