Many objects, especially these made by humans, are symmetric, e.g. cars and aeroplanes. This paper addresses the estimation of 3D structures of symmetric objects from multiple images of the same object category, e.g. different cars, seen from various viewpoints. We assume that the deformation between different instances from the same object category is non-rigid and symmetric. In this paper, we extend two leading non-rigid structure from motion (SfM) algorithms to exploit symmetry constraints. We model the both methods as energy minimization, in which we also recover the missing observations caused by occlusions. In particularly, we show that by rotating the coordinate system, the energy can be decoupled into two independent terms, which still exploit symmetry, to apply matrix factorization separately on each of them for initialization. The results on the Pascal3D+ dataset show that our methods significantly improve performance over baseline methods.
There is a long history of using symmetry as a cue for computer vision tasks. For example, symmetry has been used in depth recovery @cite_7 @cite_20 @cite_15 as well as recognizing symmetric objects @cite_34 . Several geometric clues, including symmetry, planarity, orthogonality and parallelism have been taken into account for 3D scene reconstruction @cite_19 @cite_16 , in which the author used pre-computed camera rotation matrix by vanishing point @cite_30 . Recently, symmetry has been applied in more areas such as 3D mesh reconstruction with occlusion @cite_6 , and scene reconstruction @cite_17 . For 3D keypoints reconstruction, symmetry, incorporated with planarity and compactness prior, has also been studied in @cite_28 .
@cite_30 @cite_7 @cite_28 @cite_16 @cite_6 @cite_19 @cite_15 @cite_34 @cite_20 @cite_17
2160306297 2023507039 1920849937 1529464419
Local reflection symmetry detection in nature images is a quite important but challenging task in computer vision. The main obstacle is both the scales and the orientations of symmetric structure are unknown. The multiple instance learning (MIL) framework sheds lights onto this task owing to its capability to well accommodate the unknown scales and orientations of the symmetric structures. However, to differentiate symmetry vs non-symmetry remains to face extreme confusions caused by clutters scenes and ambiguous object structures. In this paper, we propose a novel multiple instance learning framework for local reflection symmetry detection, named multiple instance subspace learning (MISL), which instead learns a group of models respectively on well partitioned subspaces. To obtain such subspaces, we propose an efficient dividing strategy under MIL setting, named partial random projection tree (PRPT), by taking advantage of the fact that each sample (bag) is represented by the proposed symmetry features computed at specific scale and orientation combinations (instances). Encouraging experimental results on two datasets demonstrate that the proposed local reflection symmetry detection method outperforms current state-of-the-arts. HighlightsWe perform clustering on samples represented by multiple instances.We learn a group of MIL classifiers on subspaces.We report state-of-the-arts results on the symmetry detection benchmark. Symmetry is an important cue for many applications, including object alignment, recognition, and segmentation. In this paper, we describe a planar reflective symmetry transform (PRST) that captures a continuous measure of the reflectional symmetry of a shape with respect to all possible planes. This transform combines and extends previous work that has focused on global symmetries with respect to the center of mass in 3D meshes and local symmetries with respect to points in 2D images. We provide an efficient Monte Carlo sampling algorithm for computing the transform for surfaces and show that it is stable under common transformations. We also provide an iterative refinement algorithm to find local maxima of the transform precisely. We use the transform to define two new geometric properties, center of symmetry and principal symmetry axes, and show that they are useful for aligning objects in a canonical coordinate system. Finally, we demonstrate that the symmetry transform is useful for several applications in computer graphics, including shape matching, segmentation of meshes into parts, and automatic viewpoint selection. The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favour as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today’s recognition systems are faced with cluttered scenes and the assumption that a closed contour exists, i.e., that figure-ground segmentation has been solved, rendering much of the medial axis community’s work inapplicable. In this article, we review a computational framework, previously reported in [1–3], that bridges the representation power of the medial axis and the need to recover and group an object’s parts in a cluttered scene. Our framework is rooted in the idea that a maximally-inscribed disc, the building block of a medial axis, can be modelled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes. A system is presented that takes a single image as an input (e.g. showing the interior of St.Peter's Basilica) and automatically detects an arbitrarily oriented symmetry plane in 3D space. Given this symmetry plane a second camera is hallucinated that serves as a virtual second image for dense 3D reconstruction, where the point of view for reconstruction can be chosen on the symmetry plane. This naturally creates a symmetry in the matching costs for dense stereo. Alternatively, we also show how to enforce the 3D symmetry in dense depth estimation for the original image. The two representations are qualitatively compared on several real world images, that also validate our fully automatic approach for dense single image reconstruction.