Towards shape from shading under realistic photographic conditions

Abstract

Abstract

Photometric stereo under perspective projection

“…The approximated equations are then combined with geometric stereo cues, and solved by minimization of an energy functional. Thus, the image irradiance equations formulated under the perspective projection model ( [22], [18], [3]) are unused.…”

“…The second and most important is that the set of equations in [4] has mixed parameters: some parameters are in image coordinates and some, in real-world coordinates. As [4] does not employ the perspective image irradiance equation ([22], [18], [3]), which expresses the reflectance map-intensity relation in image coordinates only, they need to approximate the equations using Taylor series, which they solve using iterations. The important point is that when mixed coordinates are used, even if one recovers depth derivatives correctly in real-world coordinates, one cannot directly integrate them, as the real-world grid is unknown (only the image grid is known and uniform).…”

Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations

“…Recently, a number of perspective SFS models have been considered [8,24,30], with promising applications to face reconstruction [24], reconstruction of organs [30,31], and digitization of documents [8,9]. Within the class of perspective SFS models, the one of Okatani and Deguchi [20] is distinguished by the lighting model.…”

Fast Marching Method for Generic Shape from Shading

“…r : Ω → R is a non-negative function directly related to the brightness image. From the work of Horn [11], a number of explicit PDEs corresponding to different modelings have been developed and studied [15,24,27,20,6]. By introducing the "generic" SFS equation H g (x, ∇u(x)) = 0, ∀x ∈ Ω (H g being described below), Prados and Faugeras [22,21] have recently unified a number of these explicit equations and thus their associated models.…”

“…This upgraded method seems very delicate, requires a change of variable and does not seems adaptable to more general modelings. Roughly speaking, most of the authors [13,28,6] use various techniques (e.g. changes of variables, introductions of new unknowns) in order to get back to the Eikonal equation and then to use the initial tools developed by Sethian.…”