Understanding Ourselves is the Holy Grail of the Human-Kind

Richard Feynman once said \u27what I cannot create, I do not understand\u27. It follows, that building intelligent robots that emulate us is the best way to understand the human mind

Two Correspondence Problems Easier Than One

Computer vision research rarely makes use of symmetry in stereo reconstruction despite its established importance in perceptual psychology. Such stereo reconstructions produce visually satisfying figures with precisely located points and lines, even when input images have low or moderate resolution. However, because few invariants exist, there are no known general approaches to solving symmetry correspondence on real images. The problem is significantly easier when combined with the binocular correspondence problem, because each correspondence problem provides strong non-overlapping constraints on the solution space. We demonstrate a system that leverages these constraints to produce accurate stereo models from pairs of binocular images using standard computer vision algorithms

The Role of Problem Representation in Producing Near-Optimal TSP Tours

Gestalt psychologists pointed out about 100 years ago that a key to solving difficult insight problems is to change the mental representation of the problem, as is the case, for example, with solving the six matches problem in 2D vs. 3D space. In this study we ask a different question, namely what representation is used when subjects solve search, rather than insight problems. Some search problems, such as the traveling salesman problem (TSP), are defined in the Euclidean plane on the computer monitor or on a piece of paper, and it seems natural to assume that subjects who solve a Euclidean TSP do so using a Euclidean representation. It is natural to make this assumption because the TSP task is defined in that space. We provide evidence that, on the contrary, subjects may produce TSP tours in the complex-log representation of the TSP city map. The complex-log map is a reasonable assumption here, because there is evidence suggesting that the retinal image is represented in the primary visual cortex as a complex-log transformation of the retina. It follows that the subject’s brain may be “solving” the TSP using complex-log maps. We conclude by pointing out that solving a Euclidean problem in a complex-log representation may be acceptable, even desirable, if the subject is looking for near-optimal, rather than optimal solutions

3-D Shape Recovery from a Single Camera Image

3-D shape recovery is an ill-posed inverse problem which must be solved by using a priori constraints. We use symmetry and planarity constraints to recover 3-D shapes from a single image. Once we assume that the object to be reconstructed is symmetric, all that is left to do is to estimate the plane of symmetry and establish the symmetry correspondence between the various parts of the object. The edge map of the image of an object serves as a good representation of its 2-D shape and establishing symmetry correspondence means identifying pairs of symmetric curves in the edge map. The vanishing points define the symmetry planes up to a scale factor. In this work, we have assumed that we know the vanishing points. In order to be able to match curves, we should first extract some meaningful curves, where the word meaningful implies that the curve should make sense to a human observer. Connected components obtained after canny edge detection are broken down, based on gradient orientation, to get small curve pieces which can be then combined to form meaningful curves. In order to obtain longer pieces of curves, we find the shortest paths between all pairs of short pieces of curves with a cost function that penalizes spatial separation and large turning angles. In the next step, we find the optimal curve matches that minimize the number of planes required to fit the final 3-D reconstruction while simultaneously ensuring that a substantial portion of the object is reconstructed. This optimization problem is converted to a binary integer program which is then solved using the Gurobi optimization framework. Symmetry and planarity in many ways represent the simplicity of an object and by applying these constraints we are attempting to reconstruct a simple 3-D shape that can explain the image

Spatially-global integration of closed contours by means of shortest-path in a log-polar representation

See the one page PDF with abstract and images

Combining contour and region for closed boundary extraction of a shape

This study explored human ability to extract closed boundary of a target shape in the presence of noise using spatially global operations. Specifically, we investigated the contributions of contour-based processing using line edges and region-based processing using color, as well as their interaction. Performance of the subjects was reliable when the fixation was inside the shape, and it was much less reliable when the fixation was outside. With fixation inside the shape, performance was higher when both contour and color information were present compared to when only one of them was present. We propose a biologically-inspired model to emulate human boundary extraction. The model solves the shortest (least-cost) path in the log-polar representation, a representation which is a good approximation to the mapping from the retina to the visual cortex. Boundary extraction was framed as a global optimization problem with the costs of connections calculated using four features: distance of interpolation, turning angle, color similarity and color contrast. This model was tested on some of the conditions that were used in the psychophysical experiment and its performance was similar to the performance of subjects

Figure-Ground Organization using 3D Symmetry

We present a novel approach to object localization using mirror symmetry as a general purpose and biologically motivated prior. 3D symmetry leads to good segmentation because (i) almost all objects exhibit symmetry, and (ii) configurations of objects are not likely to be symmetric unless they share some additional relationship. Furthermore, psychophysical evidence suggests that the human vision system makes use symmetry in constructing 3D percepts, indicating that symmetry may be important in object localization. No general purpose approach is known for solving 3D symmetry correspondence in 2D camera images, because few invariants exist. Therefore, to test symmetry as a clustering mechanism, we disambiguated the symmetry correspondence problem with the epipolar geometry of the binocular correspondence problem in order to simplify both. Mirror symmetry is a spatially global property that is not likely to be lost in the spatially local noise of binocular depth maps. Furthermore, each of these two correspondence problems provides non-overlapping constraints that makes it easier to solve both at once rather that each individually. We tested our approach on a corpus of 60 images collected indoors with a stereo camera system. K-means clustering was used as a baseline for comparison. The informative nature of the symmetry prior makes it possible to cluster data without a priori knowledge of which objects may appear in the scene, and without knowing how many objects there are in the scene