We develop a framework for extracting a concise representation of the shape information available from diffuse shading in a small image patch. This produces a mid-level scene descriptor, comprised of local shape distributions that are inferred separately at every image patch across multiple scales. The framework is based on a quadratic representation of local shape that, in the absence of noise, has guarantees on recovering accurate local shape and lighting. And when noise is present, the inferred local shape distributions provide useful shape information without over-committing to any particular image explanation. These local shape distributions naturally encode the fact that some smooth diffuse regions are more informative than others, and they enable efficient and robust reconstruction of object-scale shape. Experimental results show that this approach to surface reconstruction compares well against the state-of-art on both synthetic images and captured photographs.
In independent work, Kunsberg and Zucker @cite_13 have recently derived local uniqueness results that are related to, and consistent with, our results in Sec. . Their elegant analysis, which uses differential geometry and applies to continuous images, is complimentary to the discrete and algebraic approach employed in this paper. Kunsberg and Zucker also observe that the analysis of shading in patches instead of at isolated points is consistent with early processing in the visual cortex, and they discuss the possibility of local shading distributions being computed there. Indeed, the notion of such distributions is compatible with evidence that humans perceive shape in some diffuse regions more accurately than others @cite_14 .
@cite_14 @cite_13
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THE receptive fields of simple cells in mammalian primary visual cortex can be characterized as being spatially localized, oriented1–4 and bandpass (selective to structure at different spatial scales), comparable to the basis functions of wavelet transforms5,6. One approach to understanding such response properties of visual neurons has been to consider their relationship to the statistical structure of natural images in terms of efficient coding7–12. Along these lines, a number of studies have attempted to train unsupervised learning algorithms on natural images in the hope of developing receptive fields with similar properties13–18, but none has succeeded in producing a full set that spans the image space and contains all three of the above properties. Here we investigate the proposal8,12 that a coding strategy that maximizes sparseness is sufficient to account for these properties. We show that a learning algorithm that attempts to find sparse linear codes for natural scenes will develop a complete family of localized, oriented, bandpass receptive fields, similar to those found in the primary visual cortex. The resulting sparse image code provides a more efficient representation for later stages of processing because it possesses a higher degree of statistical independence among its outputs. Recently, there has been a great deal of interest in modeling the non-Gaussian structures of natural images. However, despite the many advances in the direction of sparse coding and multi-resolution analysis, the full probability distribution of pixels values in a neighborhood has not yet been described. In this study, we explore the space of data points representing the values of 3 × 3 high-contrast patches from optical and 3D range images. We find that the distribution of data is extremely “sparse” with the majority of the data points concentrated in clusters and non-linear low-dimensional manifolds. Furthermore, a detailed study of probability densities allows us to systematically distinguish between images of different modalities (optical versus range), which otherwise display similar marginal distributions. Our work indicates the importance of studying the full probability distribution of natural images, not just marginals, and the need to understand the intrinsic dimensionality and nature of the data. We believe that object-like structures in the world and the sensor properties of the probing device generate observations that are concentrated along predictable shapes in state space. Our study of natural image statistics accounts for local geometries (such as edges) in natural scenes, but does not impose such strong assumptions on the data as independent components or sparse coding by linear change of bases. Our aim is to provide a pixel-wise instance-level labeling of a monocular image in the context of autonomous driving. We build on recent work [32] that trained a convolutional neural net to predict instance labeling in local image patches, extracted exhaustively in a stride from an image. A simple Markov random field model using several heuristics was then proposed in [32] to derive a globally consistent instance labeling of the image. In this paper, we formulate the global labeling problem with a novel densely connected Markov random field and show how to encode various intuitive potentials in a way that is amenable to efficient mean field inference [15]. Our potentials encode the compatibility between the global labeling and the patch-level predictions, contrast-sensitive smoothness as well as the fact that separate regions form different instances. Our experiments on the challenging KITTI benchmark [8] demonstrate that our method achieves a significant performance boost over the baseline [32]. Recently, statistical models of natural images have shown the emergence of several properties of the visual cortex. Most models have considered the nongaussian properties of static image patches, leading to sparse coding or independent component analysis. Here we consider the basic time dependencies of image sequences instead of their nongaussianity. We show that simple-cell-type receptive fields emerge when temporal response strength correlation is maximized for natural image sequences. Thus, temporal response strength correlation, which is a nonlinear measure of temporal coherence, provides an alternative to sparseness in modeling simple-cell receptive field properties. Our results also suggest an interpretation of simple cells in terms of invariant coding principles, which have previously been used to explain complex-cell receptive fields.