All plane curves can be described at an abstract level by a sequence of five primitive elemental shapes, called "condons", which capture the sequential relations between the singular points of curvature. The condon description provides a basis for enumerating all smooth 2D curves. Let each of these smooth plane be considered as the si lhouette of an opaque 3D object. Clearly an in finity of 3D objects can generate any one of ou r "condon" silhouettes. How then can we p redict which 3D object corresponds to a g iven 2D silhouette? To restrict the infinity of choices, we impose three mathematical properties of smooth surfaces plus one simple viewing constraint. The constraint is an extension of the notion of general position, and seems to drive our preferred inferences of 3D shapes, given only the 2D contour.

Structured Light Illumination (SLI) is the process where spatially varied patterns are projected onto a 3-D surface and based on the distortion by the surface topology, phase information can be calculated and a 3D model constructed. Phase Measuring Profilometry (PMP) is a particular type of SLI that requires three or more patterns temporarily multiplexed. High speed PMP attempts to scan moving objects whose motion is small so as to have little impact on the 3-D model. Given that practically all machine vision cameras and high speed cameras employ a Field Programmable Gate Array (FPGA) interface directly to the image sensors, the opportunity exists to do the processing on camera. This thesis focuses on the design, implementation, testing, and evaluation of a camera-projector system to implement a PMP dual-frequency scheme for 3-D shape measurement on a single FPGA chip. The processor architecture is implemented and tested using the Xilinx Spartan 3 FPGA chip on an Opal Kelly development board. The hardware is described using VHDL and Verilog Hardware Description Languages (HDLs).