@conference {12452, title = {Towards view-invariant expression analysis using analytic shape manifolds}, booktitle = {2011 IEEE International Conference on Automatic Face \& Gesture Recognition and Workshops (FG 2011)}, year = {2011}, month = {2011/03/21/25}, pages = {306 - 313}, publisher = {IEEE}, organization = {IEEE}, abstract = {Facial expression analysis is one of the important components for effective human-computer interaction. However, to develop robust and generalizable models for expression analysis one needs to break the dependence of the models on the choice of the coordinate frame of the camera i.e. expression models should generalize across facial poses. To perform this systematically, one needs to understand the space of observed images subject to projective transformations. However, since the projective shape-space is cumbersome to work with, we address this problem by deriving models for expressions on the affine shape-space as an approximation to the projective shape-space by using a Riemannian interpretation of deformations that facial expressions cause on different parts of the face. We use landmark configurations to represent facial deformations and exploit the fact that the affine shape-space can be studied using the Grassmann manifold. This representation enables us to perform various expression analysis and recognition algorithms without the need for the normalization as a preprocessing step. We extend some of the available approaches for expression analysis to the Grassmann manifold and experimentally show promising results, paving the way for a more general theory of view-invariant expression analysis.}, keywords = {Databases, Deformable models, Face, face recognition, facial expression analysis, Geometry, Gold, Human-computer interaction, Manifolds, projective transformation, Riemannian interpretation, SHAPE, view invariant expression analysis}, isbn = {978-1-4244-9140-7}, doi = {10.1109/FG.2011.5771415}, author = {Taheri, S. and Turaga,P. and Chellapa, Rama} } @conference {11993, title = {Self-calibration from image derivatives}, booktitle = {Sixth International Conference on Computer Vision, 1998}, year = {1998}, month = {1998/01/04/7}, pages = {83 - 89}, publisher = {IEEE}, organization = {IEEE}, abstract = {This study investigates the problem of estimating the calibration parameters from image motion fields induced by a rigidly moving camera with unknown calibration parameters, where the image formation is modeled with a linear pinhole-camera model. The equations obtained show the flow to be clearly separated into a component due to the translation and the calibration parameters and a component due to the rotation and the calibration parameters. A set of parameters encoding the latter component are linearly related to the flow, and from these parameters the calibration can be determined. However, as for discrete motion, in the general case it is not possible, to decouple image measurements from two frames only into their translational and rotational component. Geometrically, the ambiguity takes the form of a part of the rotational component being parallel to the translational component, and thus the scene can be reconstructed only up to a projective transformation. In general, for a full calibration at least four successive image frames are necessary with the 3D-rotation changing between the measurements. The geometric analysis gives rise to a direct self-calibration method that avoids computation of optical flow or point correspondences and uses only normal flow measurements. In this technique the direction of translation is estimated employing in a novel way smoothness constraints. Then the calibration parameters are estimated from the rotational components of several flow fields using Levenberg-Marquardt parameter estimation, iterative in the calibration parameters only. The technique proposed does not require calibration objects in the scene or special camera motions and it also avoids the computation of exact correspondence. This makes it suitable for the calibration of active vision systems which have to acquire knowledge about their intrinsic parameters while they perform other tasks, or as a tool for analyzing image sequences in large video databases}, keywords = {3D-rotation, active vision, Calibration, CAMERAS, discrete motion, Encoding, Equations, image derivatives, image formation, image measurements, Image motion analysis, image motion fields, Image reconstruction, Image sequences, large video databases, Layout, Levenberg-Marquardt parameter estimation, linear pinhole-camera model, Motion estimation, Motion measurement, Optical computing, parameter estimation, projective transformation, rigidly moving camera, self-calibration, smoothness constraints, unknown calibration parameters}, isbn = {81-7319-221-9}, doi = {10.1109/ICCV.1998.710704}, author = {Brodsky, T. and Ferm{\"u}ller, Cornelia and Aloimonos, J.} }