We develop a new estimation technique for recovering depth-of-field from multiple stereo images. Depth-of-field is estimated by determining the shift in image location resulting from different camera viewpoints. When this shift is not divisible by pi
xel width, the multiple stereo images can be combined to form a super-resolution image. By modeling this super-resolution image as a realization of a random field, one can view the recovery of depth as a likelihood estimation problem. We apply these modeling techniques to the recovery of cloud height from multiple viewing angles provided by the MISR instrument on the Terra Satellite. Our efforts are focused on a two layer cloud ensemble where both layers are relatively planar, the bottom layer is optically thick and textured, and the top layer is optically thin. Our results demonstrate that with relative ease, we get comparable estimates to the M2 stereo matcher which is the same algorithm used in the current MISR standard product (details can be found in [IEEE Transactions on Geoscience and Remote Sensing 40 (2002) 1547--1559]). Moreover, our techniques provide the possibility of modeling all of the MISR data in a unified way for cloud height estimation. Research is underway to extend this framework for fast, quality global estimates of cloud height.
This paper is a continuation of arXiv:0706.3511, where we obtained a local index formula for matrix elliptic operators with shifts. Here we establish a cohomological index formula of Atiyah-Singer type for elliptic differential operators with shifts
acting between section spaces of arbitrary vector bundles. The key step is the construction of closed graded traces on certain differential algebras over the symbol algebra for this class of operators.
