Introduction - Deformable Surface 3D Reconstruction from Monocular Images - page 4

(a) (b) (c) (d)
Figure 1.5: Examples of deformed surfaces. (a) Textured and developable surface undergoing a simple
deformation. Its 3D shape can be recovered using many existing approaches that rely either on textural
or edge information. (b) Here, the sharp creases would result in failure of techniques that rely heavily on
geometric smoothness. (c,d) With much less textured surfaces whose contours may be partially occluded,
the shape of uniform parts must be inferred from that of the textured ones. This requires deformation
models that accurately represent the properties of the surfaces, or the ability to use additional cues, such
as shading.
the surface can undergo. All successful approaches to this problem exploit the fact that real surfaces
do not deform randomly and cannot assume completely irrational shapes. As a consequence, one
may introduce some knowledge of what is feasible and what is not to constrain the recovery and
resolve the ambiguities.
In this survey, we will therefore introduce a number of state-of-the-art methods that address
these issues. More specifically, we will first review the techniques that have been proposed over
the years to model the deformations of non-rigid surfaces. We will discuss their strengths and
weaknesses for monocular 3D shape recovery purposes and will introduce two more recent classes of
techniques that have been designed to overcome these weaknesses. The first includes template-based
approaches that rely on establishing correspondences with a reference image in which the shape is
known a priori . The second comprises structure-from-motion algorithms that are template-free but
require points to be tracked across video sequences. For both classes, we will first formalize the
problem and its inherent ambiguities. We will then describe the various methods that have been
introduced to overcome them. Finally, we will conclude with some perspectives on potential avenues
of research to extend the scope of all these techniques and to take them from the laboratory into the
real world.