Abstract
Many visual processes computationally amount to estimation problems. It has been shown that noise in the image data causes consistent errors in the estimation, that is statistical bias [1]. Here we analyze the effects of bias on 3D shape estimation, and we found that it predicts the perceived underestimation of slant for many settings found in experiments.
In particular, we concentrate on the problem of shape estimation from stereo using orientation disparity. We found that bias predicts the anisotropy in the perception of stereoscopic slant, an effect that has not been explained before.
It has been found that a surface slanted about the horizontal axis is estimated much easier and more accurately than a surface slanted about the vertical axis [2,3]. In both cases there is an underestimation of slant, but it is much larger for slant about the vertical. Cagnello and Rogers [2] argued that this effect is due to orientation disparity, which when the texture on the plane is made up of mostly horizontal and vertical lines, is smaller for surfaces slanting about the vertical. However as shown in [3], the effect also exists, even though in weaker form, when the texture is made up of lines oriented at 45 degrees. For such a configuration the orientation disparity in the two configurations is about the same. Thus orientation disparity by itself cannot be the cause. But errors in the estimated position and orientation of edgels cause bias, which predicts all the above findings and other parametric studies that we performed.
[1]. C. Fermuller, H. Malm. Uncertainty in visual processes predicts geometrical optical illusions, Vision Research, 44, 727-749, 2004.
[2]. R. Cagnello, B.J.Rogers. Anisotropies in the perception of stereoscopic surfaces: the role of orientation disparity. Vision Research, 33>(16): 2189-2201, 1993.
[3]. G.J. Mitchison. S.P. McKee. Mechannisms underlying the anisotropy of stereoscopic tilt perception. Vision Research, 30:1781-1791, 1990.