Statistical Analysis of Local 3D Structure in 2D Images

Abstract

Abstract

Using surfaces and surface relations in an Early Cognitive Vision system

“…For example, a step edge divides an area into two parts corresponding to different color values or texture structure. In 3D it can represent a surface edge, an orientation discontinuity or a depth discontinuity [35]. In contrast, homogeneously colored or structured image areas correspond with high likelihood to smooth 3D patches [35] and therefore homogeneous image areas can be sufficiently described by one color vector.…”

“…In 3D it can represent a surface edge, an orientation discontinuity or a depth discontinuity [35]. In contrast, homogeneously colored or structured image areas correspond with high likelihood to smooth 3D patches [35] and therefore homogeneous image areas can be sufficiently described by one color vector. Hence, both kinds of structure require different kinds of hierarchical organization (e.g., local edges can be embedded in more global contours while local texlets can be embedded in surfaces).…”

Depth Prediction at Homogeneous Image Structures

“…In (Grimson, 1982), Grimson proposed fitting square Laplacian functionals to surface orientations at existing 3D points utilizing a surface consistency constraint called 'no news is good news'. The constraint argues that if two image points do not have a contrast difference in-between, then they can be assumed to be on the same 3D surface (see (Kalkan et al, 2006) for a quantification of this assumption). (Grimson, 1982) assumes that 3D orientation is available, and the input 3D points are dense enough for second order differentiation.…”

Statistical Analysis of Second-Order Relations of 3d Structures

“…There have been only a few studies that have investigated the 3D world from range data (Howe and Purves, 2004;Huang et al, 2000;Kalkan et al, 2006;Potetz and Lee, 2003;Yang and Purves, 2003). In (Yang and Purves, 2003), the distribution of roughness, size, distance, 3D orientation, curvature and independent components of surfaces was analyzed.…”

“…In (Kalkan et al, 2006), a higher-order representation of the 2D local image patches and the 3D local patches were considered; they represented 2D images in terms of homogeneous, edge-like and corner-like structures whereas 3D range data in terms of continuities, gap discontinuities and orientation discontinuities (see section 2). With these representations, they could compute the probability P(3D Structure | 2D Structure) which among other things justifies and quantifies the assumption that if two image points do not have contrast difference inbetween, then they are likely to be coplanar.…”