# Computer Vision – From Surfaces to 3D Objects

## Cue Interpretation and Propagation: Flat versus Nonflat Visual Surfaces (Computer Vision) Part 1

Introduction In this topic, we consider what information is available to the human visual system in cases of flat and nonflat surfaces. In the case of flat surfaces, visual cues can be interpreted without any reference to surface shape; under many conditions, cue integration is well described by a linear rule; moreover, it is possible […]

## Cue Interpretation and Propagation: Flat versus Nonflat Visual Surfaces (Computer Vision) Part 2

Cue Interpretation For Nonflat Surfaces So far we described how cues are integrated at a single location and how they can be propagated to different locations along a flat or slowly curving surface. In the general case of nonflat surfaces, we have to deal with the fact that visual cues for some surface property may […]

## Symmetry, Shape, Surfaces, and Objects (Computer Vision)

Introduction Traditionally, the perception of three-dimensional (3D) scenes and objects was assumed to be the result of the reconstruction of 3D surfaces from available depth cues, such as binocular disparity, motion parallax, texture, and shading (Marr, 1982). In this approach, the role of figure-ground organization was kept to a minimum. Figure-ground organization refers to finding […]

## Noncommutative Field Theory in the Visual Cortex (Computer Vision) Part 1

Introduction We present a new mathematical model of the visual cortex, which takes into account and integrates geometric and probabilistic aspects. From a geometric point of view, the cortex has been recently described as a noncommutative Lie group, equipped with a sub-Riemannian metric (Hoffman, 1989; Ben Shahar and Zucker, 2003; Bressloff et al., 2001; Citti […]

## Noncommutative Field Theory in the Visual Cortex (Computer Vision) Part 2

The Operatorial Structure of the Cortex We will next reinterpret the neurogeometric structure introduced in the first part of the paper from a probabilistic point of view, replacing vector field generators of the Lie algebra by the corresponding operators. This operation is called in physics second quantization. FIGURE 7.5 A Kanitza triangle with curved boundaries […]

## Noncommutative Field Theory in the Visual Cortex (Computer Vision) Part 3

Probability Measure The norm of the (normalized) Bargmann transform has a probabilistic interpretation. Hence, we can interpret the norm of the output of simple cells as the probability that the image I is in a specific coherent state. More precisely, the probability that the image has a boundary with orientation 6 at the point (x, […]

## Contour-, Surface-, and Object-Related Coding in the Visual Cortex (Computer Vision) Part 1

Introduction At the early processing stages in visual cortex, information is laid out in the form of maps of the retinal image. However, contrary to intuition, uniform surfaces are not mapped by uniform distributions of neural activity. We can perceive the three-dimensional (3D) shape of a uniform surface, but stereoscopic neurons are activated only by […]

## Contour-, Surface-, and Object-Related Coding in the Visual Cortex (Computer Vision) Part 2

Border Ownership We can see from Figure 8.1 that the identification of occluding contours is important for two reasons. First, they separate features of different objects, which have to be kept separate in the processing. Second, they carry information about the shape of the occluding object. Although an occluding contour is also the boundary to […]

## Contour-, Surface-, and Object-Related Coding in the Visual Cortex (Computer Vision) Part 3

Object-Related Coding The following simple model (Craft et al., 2007) explains our findings on border ownership coding and might also help us to understand how surfaces are represented by neurons (Figure 8.9). It proposes that border ownership selectivity is produced by specific neural grouping circuits (“G cells”) that integrate contour signals of V2 neurons (“B […]

## Visual Surface Encoding: A Neuroanalytic Approach (Computer Vision) Part 1

Demand Characteristics of Visual Encoding A primary goal of visual encoding is to determine the nature and motion of the objects in the surrounding environment. In order to plan and coordinate actions, we need a functional representation of the scene layout and of the spatial configuration and the dynamics of the objects within it both […]