NYU/CNS : Faculty : Associates of CNS : Davi Geiger

I am interested in the processing of visual information in perception/recognition tasks. I work within a computational framework where the formation of patterns (groups) is driven from the data (a bottom-up process) via a hierarchical assembly of models, possibly culminating with the access to a library of stored models (memory). Each of these models process information without knowledge of the response of the next model in the hierarchy. Thus, the higher level models must request information from the lower level models (top-down process). The bottom-up process produces redundancy to create different representations of the data for easier access by the higher level models, and simultaneously removes image redundancy by grouping local features, thus reducing the complexity of the image. The top-down process aims to request information and search for the best representation of the information so as to quickly remove any image redundancy by simply assigning pointers from the library/memory to the images.

More concretely, I have been interested in prior model representations of surfaces and object shapes. Surface representation is the most basic concept that may be used to help group local features and explain bottom-up processes. I have studied the formation of illusory surfaces and methods and algorithms to compute surfaces. I formulated the problem of stereo image matching as the problem of seeking surfaces consistent with a pair of images, paying special attention to occlusions and discontinuities of these surfaces. In my formulation, the optimal matching is the one that yields the optimal surface. We have also studied the detection of junctions (e.g., corners, T-junctions, X-junctions), since these provide important local information about surface occlusions and transparency.

Object shapes provide another basic feature for recognition. I have studied geometrical properties such as the convexity of shapes. I have focused on the question: How can a given shape contour (say a contour of a frontal view of a person) be recognized, when its appearance in an image varies with viewpoint, small deformations, articulations, and possibly even partial occlusion? We have constructed new shape representations and are currently working on using them for recognition.

Methodologically, I have been interested in obtaining global characteristics based on the accumulation of local features. I create Markov random field models (MRF) of surfaces with occlusions and discontinuities. These models support an optimization framework that seeks a global optimum through local computations (e.g., dynamic programming, mean field algorithms, or EM algorithms).

E-mail: geiger@cims.nyu.edu

Selected Publications

Geiger, D. and Girosi, F. (1991) Parallel and deterministic algorithms from MRFs: surface reconstruction. IEEE Transactions Pattern Analysis and Machine Intelligence 13: 401-412
Geiger, D., Ladendorf, B., and Yuille, A. (1995) Occlusions and binocular stereo. International Journal of Computer Vision 14: 211-226
Geiger, D., Liu, T., Donahue, M., and Hummel, R. (1996) Sparse representations for image decomposition. IEEE Conference Computer Vision and Pattern Recognition, San Francisco
Ishikawa, H. and Geiger, D. (1998) Occlusions, Discontinuities and epipolar lines in stereo. Proceedings of the European Conference on Computer Vision, Freiburg, Germany
Parida, L., Geiger, D., and Hummel, R. (1998) Junctions: Detection, classification, and reconstruction. IEEE Transactions Pattern Analysis and Machine Intelligence 20: 687Ñ698
Pao, H., Geiger, D., and Rubin, N. (1999) Measuring convexity for figure/ground separation. Proceeding of the 7th IEEE International Conference on Computer Vision, 948-955
Liu, T-L. and Geiger, D. (1999) Approximate tree matching and shape similarity. Proceedings of International Conference on Computer Vision, Kerkyra, Greece
Geiger, D., Liu, T-L., and Kohn, R. (2003) Representation and self-similarity of shapes. IEEE Transactions Pattern Analysis and Machine Intelligence, in press