Many man-made objects have intrinsic symmetries and Manhattan structure. By assuming an orthographic projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and or Manhattan structure cues, which occur when the input is single- or multiple-image from the same category, e.g., multiple different cars. Specifically, analysis on the single image case implies that Manhattan alone is sufficient to recover the camera projection, and then the 3D structure can be reconstructed uniquely exploiting symmetry. However, Manhattan structure can be difficult to observe from a single image due to occlusion. To this end, we extend to the multiple-image case which can also exploit symmetry but does not require Manhattan axes. We propose a novel rigid structure from motion method, exploiting symmetry and using multiple images from the same category as input. Experimental results on the Pascal3D+ dataset show that our method significantly outperforms baseline methods.
Symmetry has been studied in computer vision for several decades. For example, symmetry has been used as a cue in depth recovery @cite_10 @cite_31 @cite_24 as well as for recognizing symmetric objects @cite_44 . Grossmann and Santos-Victor utilized various geometric clues, such as planarity, orthogonality, parallelism and symmetry, for 3D scene reconstruction @cite_29 @cite_25 , where the camera rotation matrix was pre-computed by vanishing points @cite_40 . Recently, researchers applied symmetry to scene reconstruction @cite_26 , and 3D mesh reconstruction with occlusion @cite_9 . In addition, symmetry, incorporated with planarity and compactness priors, has also been studied to reconstruct structures defined by 3D keypoints @cite_38 . By contrast, the Manhattan world assumption was developed originally for scenes @cite_19 @cite_20 @cite_21 , where the authors assumed visual scenes were based on a Manhattan 3D grid which provided 3 perpendicular axis constaints. Both symmetry and Manhattan can be straightforwardly combined, and adapted to 3D object reconstruction, particularly for man made objects.
@cite_38 @cite_26 @cite_29 @cite_9 @cite_21 @cite_24 @cite_44 @cite_40 @cite_19 @cite_31 @cite_10 @cite_25 @cite_20
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Symmetry is a powerful shape regularity that's been exploited by perceptual grouping researchers in both human and computer vision to recover part structure from an image without a priori knowledge of scene content. Drawing on the concept of a medial axis, defined as the locus of centers of maximal inscribed discs that sweep out a symmetric part, we model part recovery as the search for a sequence of deformable maximal inscribed disc hypotheses generated from a multiscale super pixel segmentation, a framework proposed by LEV09. However, we learn affinities between adjacent super pixels in a space that's invariant to bending and tapering along the symmetry axis, enabling us to capture a wider class of symmetric parts. Moreover, we introduce a global cost that perceptually integrates the hypothesis space by combining a pair wise and a higher-level smoothing term, which we minimize globally using dynamic programming. The new framework is demonstrated on two datasets, and is shown to significantly outperform the baseline LEV09. Recovering 3D geometry from a single view of an object is an important and challenging problem in computer vision. Previous methods mainly focus on one specific class of objects without large topological changes, such as cars, faces, or human bodies. In this paper, we propose a novel single view reconstruction algorithm for symmetric piece-wise planar objects that are not restricted to some object classes. Symmetry is ubiquitous in manmade and natural objects and provides rich information for 3D reconstruction. Given a single view of a symmetric piecewise planar object, we first find out all the symmetric line pairs. The geometric properties of symmetric objects are used to narrow down the searching space. Then, based on the symmetric lines, a depth map is recovered through a Markov random field. Experimental results show that our algorithm can efficiently recover the 3D shapes of different objects with significant topological variations. 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. 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.