Surface map

Abstract: This paper concerns estimation of surface maps for real scenes having a wide field of view and a wide range of depths. Much research has emphasized stereo disparity as a source of depth information. To a lesser extent, camera focus and camera vergence have also been investigated for their utility in depth recovery. We argue that these sources of visual information have mutually complementary strengths and weaknesses, and to obtain surface maps for real scenes these processes must be integrated. Such integration requires active control of camera orientations and imaging parameters to dynamically and cooperatively interleave image acquisition with surface estimation. Accordingly, a global surface map of the visual field is synthesized by systematically scanning the scene, and combining estimates of adjacent, local surface patches, each acquired by an intermediate camera configuration and having a small depth range. We present an algorithm to perform this integration, and describe its implementation on a dynamic stereo-camera imaging system. Experimental results are presented to demonstrate the superior performance of the integrated system over that of each of its components.

Abstract: Three techniques to obtain a high resolution (under 20 micron), complete, 3D surface map of an entire tooth surface are compared Stereophotogrammetric techniques can provide the required resolution but lens configurations that provide adequate spot size and MTF performance have depth of field substantially less than the length of the tooth Triangulation digitizing can provide adequate resolution but time for data acquisition is excessive Miniature mechanical linkages can provide a complete surface map in under 1 minute to a resolution of under 20 microns

Abstract: In shape analysis, finding an optimal 1-1 correspondence between 3D surfaces within a large class of admissible bijective mappings is of great importance. Such a process is called surface registration. The difficulty lies in the fact that the space of all surface diffeomorphisms is a complicated functional space, making it challenging to exhaustively search for the best mapping. To tackle this problem, we propose a simple representation of bijective surface maps using Beltrami coefficients (BCs)--complex-valued functions defined on surfaces with supremum norm less than 1. Fixing any 3 points on a pair of surfaces, there is a 1-1 correspondence between the set of surface diffeomorphisms between them and the set of BCs. Hence, every bijective surface map may be represented by a unique BC. Conversely, given a BC, we can reconstruct the unique surface map associated with it using the Beltrami Holomorphic flow (BHF) method. Using BCs to represent surface maps is advantageous because it is a much simpler functional space, which captures many essential features of a surface map. By adjusting BCs, we equivalently adjust surface diffeomorphisms to obtain the optimal map with desired properties. More specifically, BHF gives us the variation of the associated map under the variation of BC. Using this, a variational problem over the space of surface diffeomorphisms can be easily reformulated into a variational problem over the space of BCs. This makes the minimization procedure much easier. More importantly, the diffeomorphic property is always preserved. We test our method on synthetic examples and real medical applications. Experimental results demonstrate the effectiveness of our proposed algorithm for surface registration.

Abstract: A method for accurately synthesizing a full-aperture data map from a series of overlapped sub-aperture data maps. In addition to conventional alignment uncertainties, a generalized compensation framework corrects a variety of errors, including compensators that are independent in each sub-aperture. Another class of compensators (interlocked) include coefficients that are the same across all the sub-apertures. A constrained least-squares optimization routine maximizes data consistency in sub-aperture overlap regions. The stitching algorithm includes constraints representative of the accuracies of the hardware to ensure that the results are within meaningful bounds. The constraints also enable the computation of estimates of uncertainties in the final results. The method therefore automatically calibrates the system, provides a full-aperture surface map, and an estimate of residual uncertainties. Therefore, larger surfaces can be tested with greater departures from a best-fit sphere to greater accuracy than was possible in the prior art.