Image Processing in the Presence of Symmetry and Visual Perception of Surfaces (original) (raw)
Computational aspects in image analysis of symmetry and of its perception
International conference of the International Society for the Interdisciplinary Study of Symmetry ISIS-98, Haifa, Israel, Sept, 1998
Symmetry as a characteristic of shape and form has been widely studied both in the artistic and esthetic aspect on one hand and in the mathematical and computational aspect on the other. Symmetry is typically viewed as a discrete feature: an object is either symmetric or non-symmetric. However visual perception and natural behavior and phenomena treat symmetry as a continuous feature, relating to statements such as" one object is more symmetric than another" or" an object is more mirror symmetric than rotational symmetric". ...
A learning theoretic approach to perceptual geometry in natural scenes
Neurocomputing, 2001
This paper proposes a theoretical and computational framework to investigate the mathematical foundations supporting computational models, and to reconcile the biological bot-tom}up approach and cognitive top}down view of visual perception of form and space. We introduce the concept of the Gestalt of a surface that leads to perceptual estimation of geometric invariants of natural surfaces. The Gestalt of a surface is the earliest stage of representation in the brain that retains the geometrical properties of the surface encoded by optics, but adapted to the individual observer's speci"c perceptual parameters.
2009 IEEE Conference on Computer Vision and Pattern Recognition, 2009
Edge detection in images has been a fundamental problem in computer vision from its early days. Edge detection on surfaces, on the other hand, has received much less attention. The most common edges on surfaces are ridges and valleys, used for processing range images in computer vision, as well as for non-photorealistic rendering in computer graphics. We propose a new type of edges on surfaces, termed relief edges. Intuitively, the surface can be considered as an unknown smooth manifold, on top of which a local height image is placed. Relief edges are the edges of this local image. We show how to compute these edges from the local differential geometric surface properties, by fitting a local edge model to the surface. We also show how the underlying manifold and the local images can be roughly approximated and exploited in the edge detection process. Last but not least, we demonstrate the application of relief edges to artifact illustration in archaeology.
Symmetry Detection of 3D Objects
Journal of Cognitive Science, 2011
Developing realistic three-dimensional stimuli is an integral part of research on visual perception and cognition, including implicit and explicit forms of visual memory, symmetry perception, object recognition, and perceptual categorization. This is particularly important for object representation research because many theories that were developed with simplified two-dimensional stimuli turned out to be insufficient when tested with three-dimensional stimuli. In two experiments, we examined symmetry perception of naturalistic three-dimensional stimuli. The results indicate that symmetry perception for three-dimensional stimuli involves different processes from those employed for simple two-dimensional stimuli. Appendices include an archive of 3D stimuli created by 3D Studio Max (3ds Max) and a brief tutorial of the program geared for the construction of 3D stimuli for behavioral experiments.
On symmetry in visual perception
1996
This thesis is concerned with the role of symmetry in low-level image segmentation. Early detection of local image properties that could indicate the presence of an object would be useful in segmentation, and it is proposed here that approximate bilateral symmetry, which is common to many natural and man made objects, is a candidate local property. To be useful in low-level image segmentation the representation of symmetry must be relatively robust to noise interference, and the symmetry must be detectable without prior knowledge of the location and orientation of the pattern axis. His advice, support, kindness, patience, encouragement, and faith throughout the project were matched only by his sheer endurance in the finishing stages. Steve Dakin introduced me to the field of visual perception. His enthusiasm sparked my own interest, and I have alternately cursed and blessed him for this over the years. Of course, now it's almost over, I'm truly grateful. Thanks also to Steve for suggesting and discussing with me many of the ideas underlying this project, and for his friendship throughout it. I am indebted to those in the CCCN who helped with the difficult bits and made the rest a pleasure, especially to Paul Miller, my fellow journeyman, Lawrence Gerstley, for his last minute intervallic leap into the formatting, Ben Craven for reading the first draft (and not laughing out loud), and most especially to Paul Toombs for taking me dancing at the stage where most PhD students have probably forgotten how.
1993
A number of objects in the real world can be described as surfaces of revolution. These are a particular type of generalised cylinder with a straight axis whose 3D shape is formed by rotating a 2D plane about the axis. Examples of such objects are vases, many chess pieces, light bulbs, table lamps etc. This paper describes a number of techniques that can be used to recognise this class of object in a typical cluttered scene under perspective projection. Use is made of the symmetry of the occluding boundary, perceptual grouping of ellipses, 3D models and the hypothesis that an ellipse is a circle in the real world.
Multiscale Modeling & Simulation, 2003
One of the aims of computer vision in the past 30 years has been to recognize shapes by numerical algorithms. Now, what are the geometric features on which shape recognition can be based? In this paper, we review the mathematical arguments leading to a unique definition of planar shape elements. This definition is derived from the invariance requirement to not less than five classes of perturbations, namely noise, affine distortion, contrast changes, occlusion, and background. This leads to a single possibility: shape elements as the normalized, affine smoothed pieces of level lines of the image. As a main possible application, we show the existence of a generic image comparison technique able to find all shape elements common to two images.
Symmetry Detection through Entropy Minimization
2013
The world surrounding us is composed of objects. Object recognition is an important factor in our survival and functionality in the world. Through our senses, we learn the properties of objects and distinguish them from one another. We learn, in particular, that objects occupy "volume" and are bounded by "surfaces", the type of entities whose existence and properties are learned through a combination of senses. Eventually, our visual perception .of the external world relies on our ability to distinguish various pieces of surfaces, to integrate collections of surfaces into parts of an object, and to fill any missing information by inference and other mechanisms that develop as part of our survival strategy. Thus, a theory of visual perception of surfaces is at the heart of any comprehensive theory of human perceptual organization. First studied by Gestalt psychologists early in this century, perceptual organization concerns how retinal images are structured, how t...
Perception of 3D Symmetrical and Nearly Symmetrical Shapes
Symmetry, 2018
The human visual system uses priors to convert an ill-posed inverse problem of 3D shape recovery into a well-posed one. In previous studies, we have demonstrated the use of priors like symmetry, compactness and minimal surface in the perception of 3D symmetric shapes. We also showed that binocular perception of symmetric shapes can be well modeled by the above-mentioned priors and binocular depth order information. In this study, which used a shape-matching task, we show that these priors can also be used to model perception of near-symmetrical shapes. Our near-symmetrical shapes are asymmetrical shapes obtained from affine distortions of symmetrical shapes. We found that the perception of symmetrical shapes is closer to veridical than the perception of asymmetrical shapes is. We introduce a metric to measure asymmetry of abstract polyhedral shapes, and a similar metric to measure shape dissimilarity between two polyhedral shapes. We report some key observations obtained by analyzin...
Geometric Surface Processing via Normal Maps
ACM Transactions on Graphics, 1998
Importance w/ 300 samples Importance w/ 3000 samples Structured importance w/ 300 samples Structured importance w/ 4.7 rays/pixel : Close-up rendering of a glossy buddha in the grace cathedral environment. The two images on the left have been rendered using stratified importance sampling with 300 and 3000 samples, while the two images on the right show the result of structured importance sampling using 300 samples, and after further rendering optimizations an average of 4.7 rays per pixel to evaluate the 300 possible samples.
Acta Psychologica, 2008
Numerous models of symmetry perception have been proposed in recent years. Unfortunately, it is difficult to assess the relative utility of these models as little effort has been made to directly compare them. This paper outlines a new model of symmetry perception based upon the relational structure revealed by Voronoi tessellation. The model has been developed in response to evidence suggesting that the human visual system is generating a Voronoi-like representation at an early stage in processing. Bayesian model selection is employed to compare the performance of the Voronoi model to that of five previously published models across six empirical datasets. The results indicate that the Voronoi model provides a more likely account of the data than the five alternative models.
Detecting mirror-symmetry of a volumetric shape from its single 2D image
2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, 2008
We present a new computational model for verifying whether a 3D shape is mirror-symmetric based on its single 2D image. First, a psychophysical experiment which tested human performance in detection of 3D symmetry is described. These psychophysical results led to the formulation of a new algorithm for symmetry detection. The algorithm first recovers the 3D shape using a priori constraints (symmetry, planarity of contours and 3D compactness) and then evaluates the degree of symmetry of the 3D shape. Reliable discrimination by the algorithm between symmetric and asymmetric 3D shapes involves two measures: similarity of the two halves of a 3D shape and compactness of the 3D shape. Performance of this algorithm is highly correlated with that of the subjects. We conclude that this algorithm is a plausible model of the mechanisms used by the human visual system.
Perception of surfaces from line drawings
Displays, 2007
We test the perception of 3D surfaces that have been rendered by a set of lines drawn on the surface. Each surface is rendered as a family of curves which are in the simplest case the intersections with a family of parallel planes. On each trial, a surface or its "distorted" version is shown in this way, in an arbitrary orientation on an LCD screen or in a volumetric 3D display. The distortion is produced by stretching the surface in the z-direction by 30%. The subject's task is to decide whether two sequentially presented surfaces are identical or not. The subject's performance is measured by the discriminability d', which is a conventional dependent variable in signal detection experiments. The work investigates the question whether a surface rendered with planar and geodesic curves is easier to recognize than one where the curves are not planar or not geodesic.
On Reflection Symmetry In Natural Images
Proceedings of the 15th International Workshop on Content-Based Multimedia Indexing
Many new symmetry detection algorithms have been recently developed, thanks to an interest revival on computational symmetry for computer graphics and computer vision applications. Notably, in 2013 the IEEE CVPR Conference organized a dedicated workshop and an accompanying symmetry detection competition. In this paper we propose an approach for symmetric object detection that is based both on the computation of a symmetry measure for each pixel and on saliency. The symmetry value is obtained as the energy balance of the even-odd decomposition of a patch w.r.t. each possible axis. The candidate symmetry axes are then identified through the localization of peaks along the direction perpendicular to each considered axis orientation. These found candidate axes are finally evaluated through a confidence measure that also allow removing redundant detected symmetries. The obtained results within the framework adopted in the aforementioned competition show significant performance improvement.
Radial Symmetry Detection and Shape Characterization with the Multiscale Area Projection Transform
Computer Graphics Forum, 2012
We present a novel method to characterize 3D surfaces through the computation of a function called (Multiscale) Area Projection Transform, measuring the likelihood of points in the 3D space to be center of radial symmetry at selected scales (radii). The function is derived through a simple geometric framework based on parallel surfaces and can be easily computed on triangulated meshes. It measures locally the area of the surface well approximated by a sphere of radius R centered in the point and can be normalized in order to obtain a scale invariant radial symmetry enhancement transform. This transform can therefore be used to detect and characterize salient regions like approximately spherical and approximately cylindrical surface parts and, being the transform robust against holes and missing parts, it is suitable for real world applications e.g. anatomical features detection. Furthermore, its histograms can be effectively used to build a global shape descriptor that provides very good results in shape retrieval experiments.
Shape from shaded random surfaces
Vision Research, 1995
The perception of surface relief from random shading patterns is measured by having observers adjust three-dimensional local probes, the projections of which are superimposed on the image. Three observers perform four settings of 91 probes on each of 14 images. These images are generated by calculating the Lambertian reflectance of a random superposition of elliptical Gaussian hills and valleys illuminated by a single distant light source as well as by ambient light. Neither the surfaee reflectance equation nor the light source direction is conveyed to our observers in any way. Mathematically, this "pure" shape-from-shading problem has highly non-uniqne solutions. Perception of a well-defined, stable shape therefore implies that the ambiguity is resolved, i.e. a gauge is fixed. We analyse the surface ambiguity or gauge freedom which is left unconstrained by pure shading information and we investigate possible ways of restricting it. Statistical analysis of the curl component of the field of probe settings reveals that the settings are significantly consistent with an underlying perceived surface. In spite of the large theoretical ambiguity in the stimuli, the settings are reproducible and show considerable inter-observer agreement. Even the correlation of the settings with the real surfaces is surprisingly large. If the settings are compared to the real surface normals, one finds a series of biases, the strongest of which is that the global sudace slant is systematically underestimated, even in those cases where ending occluding contours or high-contrast luminance ridges, indicative of "almost" contours, are present in the image. Another bias then is that the corresponding rims on the surface are seen as roughly parallel to the picture plane.