Mathieu Perriollat

Generalized Thin-Plate Spline Warps

The Thin-Plate Spline warp has been shown to be a very effective parameterized model of the optic flow field between images of various types of deformable surfaces, such as a paper sheet being bent. Recent work has also used such warps for images of a smooth and rigid surface. Standard Thin-Plate Spline warps are however not rigid, in the sense that they do not comply with the epipolar geometry. They are also intrinsically affine, in the sense of the affine camera model, since they are not able to simply model the effect of perspective projection.We propose three types of warps based on the Thin-Plate Spline. The first one is a rigid flexible warp. It describes the optic flow field induced by a smooth and rigid surface, and satisfies the affine epipolar geometry constraint. The second and third proposed warps extend the standard Thin-Plate Spline warp and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details and a hierarchy is defined. Experimental results on simulated and real data are reported.

A Quasi-Minimal Model for Paper-Like Surfaces

Smoothly bent paper-like surfaces are developable. They are however difficult to minimally parameterize since the number of meaningful parameters is intrinsically dependent on the actual deformation. Previous generative models are either incomplete, i.e. limited to subsets of developable surfaces, or depend on huge parameter sets. We propose a generative model governed by a quasi-minimal set of intuitive parameters, namely rules and angles. More precisely, a flat mesh is bent along guiding rules, while a number of extra rules controls the level of smoothness. The generated surface is guaranteed to be developable. A fully automatic multi-camera three dimensional reconstruction algorithm, including model-based bundle-adjustment, demonstrates our model on real images.

Generalized Thin-Plate SplineWarps

Thin-plate spline warps have been shown to be very effective as a parameterized model of the optic flow field between images of various deforming surfaces. Examples include a sheet of paper being manually handled. Recent work has used such warps for images of smooth rigid surfaces. Standard thin-plate spline warps are not rigid, in the sense that they do not satisfy the epipolar geometry constraint, and are intrinsically affine, in the sense of the affine camera model. We propose three types of warps based on the thin-plate spline. The first one is a flexible rigid warp. It describes the optic flow field induced by a smooth rigid surface, and satisfies the affine epipolar geometry constraint. The second and third ones extend the standard thin-plate spline and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details, and a hierarchy is defined. Experimental results on simulated and real data are reported, showing that the proposed warps outperform the standard one in several cases of interest.

Industrial Phase-Shifting Profilometry in Motion

Phase-Shift Profilometry (PSP) provides a means for dense high-quality surface scanning. However it imposes a staticity constraint: The scene is required to remain still during the acquisition of multiple images. PSP is also not applicable to dynamic scenes. On the other hand, there exist active stereo techniques which overcome these constraints but impose other limitations, for instance on the surface’s continuity or texture, or by significantly reducing the reconstruction’s resolution.