Browsing by Author "Nagar, Rajendra"

Reflection symmetry is a very commonly occurring feature in both natural and man-made objects, which helps in understanding objects better and makes them visually pleasing. Detection of reflection symmetry is a fundamental problem in the field of computer vision and computer graphics which aids in understanding and representing reflective symmetric objects. In this work, we attempt the problem of detecting the 3D global reflection symmetry of a 3D object represented as a point cloud. The main challenge is to handle outliers, missing parts, and perturbations from the perfect reflection symmetry. We propose a descriptor-free approach, in which, we pose the problem of reflection symmetry detection as an optimization problem and provide a closed-form solution. We show that the proposed method achieves state-of-the-art performance on the standard dataset.

We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to Rd containing a distorted reflection symmetry pattern. We pose the problem of detecting approximate reflection symmetry as the problem of establishing the correspondences between the points which are reflections of each other and determining 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 an optimization problem on a smooth Riemannian product manifold. The proposed approach estimates the symmetry from the distribution of the points and is descriptor independent. We evaluate 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 reflection symmetry detection along with relevant comparisons.

We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to 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.

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.

In this work, we address the problem of extracting high dimensional, soft semantic feature descriptors for every pixel in an image using a deep learning framework. Existing methods rely on a metric learning objective called multi-class N-pair loss, which requires pairwise comparison of positive examples (same class pixels) to all negative examples (different class pixels). Computing this loss for all possible pixel pairs in an image leads to a high computational bottleneck. We show that this huge computational overhead can be reduced by learning this metric based on superpixels. This also conserves the global semantic context of the image, which is lost in pixel-wise computation because of the sampling to reduce comparisons. We design an end-to-end trainable network with a loss function and give a detailed comparison of two feature extraction methods: pixel-based and superpixel-based. We also investigate hard semantic labeling of these soft semantic feature descriptors.

Reflection symmetry is one of the most commonly occurring and prominent visual attributes present in the real world. With an increase in the display devices of different sizes and aspect ratios, the images captured from the real world need to be resized to fit to the display device. In this paper, we propose a novel image retargeting approach which preserves the reflection symmetry present in the image during the image retargeting process. We detect the symmetry region present in the image using symmetry axis detection and object proposals. We propose a novel framework for finding an optimized reflected seam for the least energy seam defined by the seam carving approach. The symmetry axis and the symmetric object are preserved by adding or removing a seam and its reflected counterpart together. We show better preservation of symmetry axis, preservation of shape of the symmetric object, and quality of image retargeting when compared to the existing methods using three quantitative measures along with the qualitative results.

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.

Reflection symmetry is ubiquitous in nature and plays an important role in object detection and recognition tasks. Most of the existing methods for symmetry detection extract and describe each keypoint using a descriptor and a mirrored descriptor. Two keypoints are said to be mirror symmetric key-points if the original descriptor of one keypoint and the mirrored descriptor of the other keypoint are similar. However, these methods suffer from the following issue. The background pixels around the mirror symmetric pixels lying on the boundary of an object can be different. Therefore, their descriptors can be different. However, the boundary of a symmetric object is a major component of global reflection symmetry. We exploit the estimated boundary of the object and describe a boundary pixel using only the estimated normal of the boundary segment around the pixel. We embed the symmetry axes in a graph as cliques to robustly detect the symmetry axes. We show that this approach achieves state-of-the-art results in a standard dataset.

Reflection symmetry is present in most of the man-made or naturally formed objects. In computer vision, real-world scenes are represented by dense 3-D models or by 2-D projections, such as images captured by cameras. Most of the existing methods either detect reflection symmetry from dense 3-D models or 2-D projections. However, generating a dense 3-D model is a computationally expensive process and reflection symmetry may not be evident in any of the 2-D views obtained through projections. In this letter, we propose an energy minimizationbased approach to detect the reflection symmetry present in the object from its multiple 2-D projections captured from different viewpoints and the sparse 3-D model obtained using these projections. The proposed approach only estimates the sparse 3-D model and utilizes content of the images in terms of local scale invariant features. The energy minimization problem reduces to the problem of finding the eigenvector corresponding to the smallest eigenvalue of a small matrix, thereby leading to reduction in computations.

Autonomous assembly of objects is an essential task in robotics and 3D computer vision. It has been studied extensively in robotics as a problem of motion planning, actuator control and obstacle avoidance. However, the task of developing a generalized framework for assembly robust to structural variants remains relatively unexplored. In this work, we tackle this problem using a recurrent graph learning framework considering inter-part relations and the progressive update of the part pose. Our network can learn more plausible predictions of shape structure by accounting for priorly assembled parts. Compared to the current state-of-the-art, our network yields up to 10% improvement in part accuracy and up to 15% improvement in connectivity accuracy on the PartNet [23] dataset. Moreover, our resulting latent space facilitates exciting applications such as shape recovery from the point-cloud components. We conduct extensive experiments to justify our design choices and demonstrate the effectiveness of the proposed framework.

Autonomous assembly of objects is an essential task in robotics and 3D computer vision. It has been studied extensively in robotics as a problem of motion planning, actuator control and obstacle avoidance. However, the task of developing a generalized framework for assembly robust to structural variants remains relatively unexplored. In this work, we tackle this problem using a recurrent graph learning framework considering inter-part relations and the progressive update of the part pose. Our network can learn more plausible predictions of shape structure by accounting for priorly assembled parts. Compared to the current state-of-the-art, our network yields up to 10% improvement in part accuracy and up to 15% improvement in connectivity accuracy on the PartNet dataset. Moreover, our resulting latent space facilitates exciting applications such as shape recovery from the point-cloud components. We conduct extensive experiments to justify our design choices and demonstrate the effectiveness of the proposed framework.

We have developed a novel method for image abstraction which preserves more details present in the salient regions and removes details present in the non-salient regions from the given image of a natural scene. We define a region to be salient based on the saliency measure estimated in the region. We propose to preserve details in salient regions by dividing them into smaller groups of pixels and remove details from non-salient regions by dividing them in larger group of pixels. We achieve this kind of grouping by guiding an over-segmentation algorithm with spatially varying block size depending on the saliency measure. The adaptive image abstraction goal is finally achieved using a novel brush called point spread brush which is used to reproduce the action of brush with a varying spatial spread.

Over-segmentation of an image into superpixels has become an useful tool for solving various problems in computer vision. Reflection symmetry is quite prevalent in both natural and man-made objects. Existing algorithms for estimating superpixels do not preserve the reflection symmetry of an object which leads to different sizes and shapes of superpixels across the symmetry axis. In this work, we propose an algorithm to over-segment an image through the propagation of reflection symmetry evident at the pixel level to superpixel boundaries. In order to achieve this goal, we exploit the detection of a set of pairs of pixels which are mirror reflections of each other. We partition the image into superpixels while preserving this reflection symmetry information through an iterative algorithm. We compare the proposed method with state-of-the-art superpixel generation methods and show the effectiveness of the method in preserving the size and shape of superpixel boundaries across the reflection symmetry axes. We also present an application called unsupervised symmetric object segmentation to illustrate the effectiveness of the proposed approach.