TY - CONF T1 - The statistics of optical flow: implications for the process of correspondence in vision T2 - 15th International Conference on Pattern Recognition, 2000. Proceedings Y1 - 2000 A1 - Fermüller, Cornelia A1 - Aloimonos, J. KW - Bias KW - Computer vision KW - correlation KW - correlation methods KW - energy-based method KW - flow estimation KW - Frequency estimation KW - gradient method KW - gradient methods KW - Image analysis KW - Image motion analysis KW - Image sequences KW - least squares KW - least squares approximations KW - Motion estimation KW - Nonlinear optics KW - Optical feedback KW - optical flow KW - Optical harmonic generation KW - Optical noise KW - Statistics KW - Visual perception AB - This paper studies the three major categories of flow estimation methods: gradient-based, energy-based, and correlation methods; it analyzes different ways of compounding 1D motion estimates (image gradients, spatio-temporal frequency triplets, local correlation estimates) into 2D velocity estimates, including linear and nonlinear methods. Correcting for the bias would require knowledge of the noise parameters. In many situations, however, these are difficult to estimate accurately, as they change with the dynamic imagery in unpredictable and complex ways. Thus, the bias really is a problem inherent to optical flow estimation. We argue that the bias is also integral to the human visual system. It is the cause of the illusory perception of motion in the Ouchi pattern and also explains various psychophysical studies of the perception of moving plaids. Finally, the implication of the analysis is that flow or correspondence can be estimated very accurately only when feedback is utilized JA - 15th International Conference on Pattern Recognition, 2000. Proceedings PB - IEEE VL - 1 SN - 0-7695-0750-6 M3 - 10.1109/ICPR.2000.905288 ER - TY - CONF T1 - Independent motion: the importance of history T2 - Computer Vision and Pattern Recognition, 1999. IEEE Computer Society Conference on. Y1 - 1999 A1 - Pless, R. A1 - Brodsky, T. A1 - Aloimonos, J. KW - aerial visual surveillance KW - background image KW - Fluid flow measurement KW - Frequency measurement KW - History KW - Motion detection KW - Motion estimation KW - Motion measurement KW - Noise measurement KW - Optical computing KW - Optical noise KW - spatiotemporal image intensity gradient measurements KW - Spatiotemporal phenomena KW - Surveillance KW - Video sequences AB - We consider a problem central in aerial visual surveillance applications-detection and tracking of small, independently moving objects in long and noisy video sequences. We directly use spatiotemporal image intensity gradient measurements to compute an exact model of background motion. This allows the creation of accurate mosaics over many frames and the definition of a constraint violation function which acts as an indication of independent motion. A novel temporal integration method maintains confidence measures over long subsequences without computing the optic flow, requiring object models, or using a Kalman filler. The mosaic acts as a stable feature frame, allowing precise localization of the independently moving objects. We present a statistical analysis of the effects of image noise on the constraint violation measure and find a good match between the predicted probability distribution function and the measured sample frequencies in a test sequence JA - Computer Vision and Pattern Recognition, 1999. IEEE Computer Society Conference on. PB - IEEE VL - 2 SN - 0-7695-0149-4 M3 - 10.1109/CVPR.1999.784614 ER - TY - CONF T1 - Statistical biases in optic flow T2 - Computer Vision and Pattern Recognition, 1999. IEEE Computer Society Conference on. Y1 - 1999 A1 - Fermüller, Cornelia A1 - Pless, R. A1 - Aloimonos, J. KW - Distributed computing KW - Frequency domain analysis KW - HUMANS KW - image derivatives KW - Image motion analysis KW - Image sequences KW - Least squares methods KW - Motion estimation KW - Optical computing KW - Optical distortion KW - optical flow KW - Optical noise KW - Ouchi illusion KW - perception of motion KW - Psychology KW - Spatiotemporal phenomena KW - statistical analysis KW - systematic bias KW - total least squares AB - The computation of optical flow from image derivatives is biased in regions of non uniform gradient distributions. A least-squares or total least squares approach to computing optic flow from image derivatives even in regions of consistent flow can lead to a systematic bias dependent upon the direction of the optic flow, the distribution of the gradient directions, and the distribution of the image noise. The bias a consistent underestimation of length and a directional error. Similar results hold for various methods of computing optical flow in the spatiotemporal frequency domain. The predicted bias in the optical flow is consistent with psychophysical evidence of human judgment of the velocity of moving plaids, and provides an explanation of the Ouchi illusion. Correction of the bias requires accurate estimates of the noise distribution; the failure of the human visual system to make these corrections illustrates both the difficulty of the task and the feasibility of using this distorted optic flow or undistorted normal flow in tasks requiring higher lever processing JA - Computer Vision and Pattern Recognition, 1999. IEEE Computer Society Conference on. PB - IEEE VL - 1 SN - 0-7695-0149-4 M3 - 10.1109/CVPR.1999.786994 ER -