Integration of shading and texture cues: testing the linear model

One of the first attempts to develop a formal model of depth cue integration is to be found in Maloney and Landy's (1989) "human depth combination rule". They advocate that the combination of depth cues by the visual sysetem is best described by a weighted linear model. The present experiments tested whether the linear combination rule applies to the integration of texture and shading. As would be predicted by a linear combination rule, the weight assigned to the shading cue did vary as a function of its curvature value. However, the weight assigned to the texture cue varied systematically as a function of the curvature value of both cues. Here we descrive a non-linear model which provides a better fit to the data. Redescribing the stimuli in terms of depth rather than curvature reduced the goodness of fit for all models tested. These results support the hypothesis that the locus of cue integration is a curvature map, rather than a depth map. We conclude that the linear comination rule does not generalize to the integration of shading and texture, and that for these cues it is likely that integration occurs after the recovery of surface curvature.

Speech Recognition with unknown partial feature corruption - a review of the union model

This paper provides a summary of our studies on robust speech recognition based on a new statistical approach – the probabilistic union model. We consider speech recognition given that part of the acoustic features may be corrupted by noise. The union model is a method for basing the recognition on the clean part of the features, thereby reducing the effect of the noise on recognition. To this end, the union model is similar to the missing feature method. However, the two methods achieve this end through different routes. The missing feature method usually requires the identity of the noisy data for noise removal, while the union model combines the local features based on the union of random events, to reduce the dependence of the model on information about the noise. We previously investigated the applications of the union model to speech recognition involving unknown partial corruption in frequency band, in time duration, and in feature streams. Additionally, a combination of the union model with conventional noise-reduction techniques was studied, as a means of dealing with a mixture of known or trainable noise and unknown unexpected noise. In this paper, a unified review, in the context of dealing with unknown partial feature corruption, is provided into each of these applications, giving the appropriate theory and implementation algorithms, along with an experimental evaluation.

Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.