We show that two important properties of the primary visual cortex emerge when the principle of temporal coherence is applied to natural image sequences. The properties are simple-cell-like receptive fields and complex-cell-like pooling of simple cell outputs, which emerge when we apply two different approaches to temporal coherence. In the first approach we extract receptive fields whose outputs are as temporally coherent as possible. This approach yields simple-cell-like receptive fields (oriented, localized, multiscale). Thus, temporal coherence is an alternative to sparse coding in modeling the emergence of simple cell receptive fields. The second approach is based on a two-layer statistical generative model of natural image sequences. In addition to modeling the temporal coherence of individual simple cells, this model includes inter-cell temporal dependencies.

In [1] we introduced a linear statistical model of joint color changes in images due to variation in lighting and certain non-geometric camera parameters. We did this by measuring the mappings of colors in one image of a scene to colors in another image of the same scene under different lighting conditions. Here we increase the flexibility of this color flow model by allowing flow coefficients to vary according to a low order polynomial over the image. This allows us to better fit smoothly varying lighting conditions as well as curved surfaces without endowing our model with too much capacity. We show results on image matching and shadow removal and detection.

The problem of super-resolution involves generating feasible higher resolution images, which are pleasing to the eye and realistic, from a given low resolution image. This might be attempted by using simple filters for smoothing out the high resolution blocks or through applications where substantial prior information is used to imply the textures and shapes which will occur in the images. In this paper we describe an approach which lies between the two extremes. It is a generic unsupervised method which is usable in all domains, but goes beyond simple smoothing methods in what it achieves. We use a dynamic treelike architecture to model the high resolution data. Approximate conditioning on the low resolution image is achieved through a mean field approach.

We present an algorithm that uses multiple cues to recover shading and reflectance intrinsic images from a single image. Using both color information anda classifier trained to recognize gray-scale patterns, each image derivative is classified as being caused by shading or a change in the surface's reflectance. Generalized Belief Propagation is then used to propagate information from areas where the correct classification is clear to areas where it is ambiguous. We also show results on real images.

Recent algorithms for sparse coding and independent component analysis (ICA)have demonstrated how localized features can be learned from natural images. However, these approaches do not take image transformations intoaccount. As a result, they produce image codes that are redundant because the same feature is learned at multiple locations. We describe an algorithm for sparse coding based on a bilinear generative model of images. By explicitly modeling the interaction between image featuresand their transformations, the bilinear approach helps reduce redundancy in the image code and provides a basis for transformationinvariant vision.We present results demonstrating bilinear sparse coding of natural images. We also explore an extension of the model that can capture spatial relationships between the independent features of an object, therebyproviding a new framework for parts-based object recognition.

We propose a model that can learn parts-based representations of high-dimensional data.

The goal of low-level vision is to estimate an underlying scene, given an observed image. Real-world scenes (eg, albedos or shapes) can be very complex, conventionally requiring high dimensional representations which are hard to estimate and store. We propose a low-dimensional representation, calleda scene recipe, that relies on the image itself to describe the complex scene configurations. Shape recipes are an example: these are the regression coefficients that predict the bandpassed shape from image data. We describe the benefits of this representation, and show two uses illustrating their properties: (1) we improve stereo shape estimates by learning shape recipes at low resolution and applying them at full resolution; (2) Shape recipes implicitly contain information about lighting and materials and we use them for material segmentation.

We show that two important properties of the primary visual cortex emerge when the principle of temporal coherence is applied to natural image sequences. The properties are simple-cell-like receptive fields and complex-cell-like pooling of simple cell outputs, which emerge when we apply two different approaches to temporal coherence. In the first approach we extract receptive fields whose outputs are as temporally coherent aspossible. This approach yields simple-cell-like receptive fields (oriented, localized, multiscale). Thus, temporal coherence is an alternative tosparse coding in modeling the emergence of simple cell receptive fields. The second approach is based on a two-layer statistical generative model of natural image sequences. In addition to modeling the temporal coherence of individual simple cells, this model includes inter-cell temporal dependencies.Estimation of this model from natural data yields both simple-cell-like receptive fields, and complex-cell-like pooling of simple cell outputs. In this completely unsupervised learning, both layers ofthe generative model are estimated simultaneously from scratch. This is a significant improvement on earlier statistical models of early vision, where only one layer has been learned, and others have been fixed a priori.

We describe a method for learning sparse multiscale image representations usinga sparse prior distribution over the basis function coefficients. The prior consists of a mixture of a Gaussian and a Dirac delta function, and thus encourages coefficients to have exact zero values. Coefficients for an image are computed by sampling from the resulting posterior distribution with a Gibbs sampler. The learned basis is similar to the Steerable Pyramid basis, and yields slightly higher SNR for the same number of active coefficients. Denoising usingthe learned image model is demonstrated for some standard test images, with results that compare favorably with other denoising methods.

The extraction of a single high-quality image from a set of lowresolution imagesis an important problem which arises in fields such as remote sensing, surveillance, medical imaging and the extraction ofstill images from video. Typical approaches are based on the use of cross-correlation to register the images followed by the inversion of the transformation from the unknown high resolution imageto the observed low resolution images, using regularization toresolve the ill-posed nature of the inversion process. In this paper we develop a Bayesian treatment of the super-resolution problem in which the likelihood function for the image registration parametersis based on a marginalization over the unknown high-resolution image. This approach allows us to estimate the unknown point spread function, and is rendered tractable through the introduction of a Gaussian process prior over images. Results indicate a significant improvement over techniques based on MAP (maximum a-posteriori) point optimization of the high resolution image and associated registration parameters. 1 Introduction