Visual Encoding The 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 dynamics of the scene layout and of the spatial configuration and the dynamics of the objects within it. The […]

# Computer Vision – From Surfaces to 3D Objects

## Introduction: The Role of Midlevel Surface Representation in 3D Object Encoding (Computer Vision) Part 2

Surface Representation as a Riemannian Fiber Bundle Jun Zhang has made the interesting proposal that visual perception can be viewed as an interpretation based on the intrinsic geometry determined by rules of organization of the sensory data (Zhang and Wu, 1990; Zhang, 2005). The general idea is to relate perceptual unity to the concept of […]

## Scene Statistics and 3D Surface Perception (Computer Vision) Part 1

Introduction The inference of depth information from single images is typically performed by devising models of image formation based on the physics of light interaction and then inverting these models to solve for depth. Once inverted, these models are highly underconstrained, requiring many assumptions, such as Lambertian surface reflectance, smoothness of surfaces, uniform albedo, or […]

## Scene Statistics and 3D Surface Perception (Computer Vision) Part 2

Implications toward depth inference Armed with a better understanding of the statistics of real scenes, we are better prepared to develop successful depth inference algorithms. One example is range image superresolution. Often, we may have a high-resolution color image of a scene but only a low spatial resolution range image (range images record the 3D […]

## Mechanisms for Propagating Surface Information in 3D Reconstruction (Computer Vision) Part 1

Introduction Bayesian and other related statistical techniques have emerged as a dominant paradigm in computer vision for estimating three-dimensional (3D) surfaces in the presence of noisy and sparse depth cues. In particular, for 3D reconstruction problems, these techniques have been implemented using Markov random fields (MRFs), which are probabilistic models that express how variables arranged […]

## Mechanisms for Propagating Surface Information in 3D Reconstruction (Computer Vision) Part 2

Learning MRF Parameters The MRF model in the “Markov Random Fields for Stereo” section above has a number of free parameters (such as ß, t, and ß) that must be set correctly for the model to be realistic and accurate enough to make good inferences. There are well-established procedures (Scharstein and Pal, 2005) for learning […]

## 3D Surface Representation Using Ricci Flow (Computer Vision) Part 1

Introduction 3D Surface Representation Three-dimensional (3D) surface representation plays a fundamental role in middle-level vision. In this work, a representation of 3D surfaces based on modern geometry is introduced. According to Felix Klein’s Erlangen program, different geometries study the invariants under different transformation groups. Given a surface embedded in 3D Euclidean space, S M3, intrinsically, […]

## 3D Surface Representation Using Ricci Flow (Computer Vision) Part 2

Smooth Surface Ricci Flow Suppose S is a smooth surface with a Riemannian metric g. The Ricci flow deforms the metric g(t) according to the Gaussian curvature K(t) (induced by itself), where t is the time parameter: There is an analogy between the Ricci flow and the heat diffusion process. Suppose T(t) is a temperature […]

## 3D Surface Representation Using Ricci Flow (Computer Vision) Part 3

Discrete Surface Ricci Flow Suppose (X , O) is a weighted mesh with an initial circle packing metric. The discrete Ricci flow is defined as follows: whereis the user-defined target curvature. The dis crete Ricci flow has the same form as the smooth Ricci flow (Equation [4.2]), which deforms the circle packing metric according to […]

## 3D Surface Representation Using Ricci Flow (Computer Vision) Part 4

Applications The 3D surface conformal representation using Ricci flow has broad applications. Conformal Brain Mapping In medical imaging, it is helpful to compare different cortex surfaces for monitoring the progress of neurological diseases or for diagnosing the potential abnormality. FIGURE 4.10 Hyperbolic Yamabe flow for surface with negative Euler number. (a) and (b) The left […]