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93
Relations between the statistics of natural images and the response properties of cortical cells
 J. Opt. Soc. Am. A
, 1987
"... The relative efficiency of any particular imagecoding scheme should be defined only in relation to the class of images that the code is likely to encounter. To understand the representation of images by the mammalian visual system, it might therefore be useful to consider the statistics of images f ..."
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Cited by 605 (13 self)
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The relative efficiency of any particular imagecoding scheme should be defined only in relation to the class of images that the code is likely to encounter. To understand the representation of images by the mammalian visual system, it might therefore be useful to consider the statistics of images from the natural environment (i.e., images with trees, rocks, bushes, etc). In this study, various coding schemes are compared in relation to how they represent the information in such natural images. The coefficients of such codes are represented by arrays of mechanisms that respond to local regions of space, spatial frequency, and orientation (Gaborlike transforms). For many classes of image, such codes will not be an efficient means of representing information. However, the results obtained with six natural images suggest that the orientation and the spatialfrequency tuning of mammalian simple cells are well suited for coding the information in such images if the goal of the code is to convert higherorder redundancy (e.g., correlation between the intensities of neighboring pixels) into firstorder redundancy (i.e., the response distribution of the coefficients). Such coding produces a relatively high signaltonoise ratio and permits information to be transmitted with only a subset of the total number of cells. These results support Barlow's theory that the goal of natural vision is to represent the information in the natural environment with minimal redundancy.
PyramidBased Texture Analysis/Synthesis
, 1995
"... This paper describes a method for synthesizing images that match the texture appearanceof a given digitized sample. This synthesis is completely automatic and requires only the "target" texture as input. It allows generation of as much texture as desired so that any object can be covered. It can be ..."
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Cited by 386 (0 self)
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This paper describes a method for synthesizing images that match the texture appearanceof a given digitized sample. This synthesis is completely automatic and requires only the "target" texture as input. It allows generation of as much texture as desired so that any object can be covered. It can be used to produce solid textures for creating textured 3d objects without the distortions inherent in texture mapping. It can also be used to synthesize texture mixtures, images that look a bit like each of several digitized samples. The approach is based on a model of human texture perception, and has potential to be a practically useful tool for graphics applications. 1 Introduction Computer renderings of objects with surface texture are more interesting and realistic than those without texture. Texture mapping [15] is a technique for adding the appearance of surface detail by wrapping or projecting a digitized texture image ontoa surface. Digitized textures can be obtained from a variety ...
Optimal Unsupervised Learning in a SingleLayer Linear Feedforward Neural Network
, 1989
"... A new approach to unsupervised learning in a singlelayer linear feedforward neural network is discussed. An optimality principle is proposed which is based upon preserving maximal information in the output units. An algorithm for unsupervised learning based upon a Hebbian learning rule, which achie ..."
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Cited by 219 (0 self)
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A new approach to unsupervised learning in a singlelayer linear feedforward neural network is discussed. An optimality principle is proposed which is based upon preserving maximal information in the output units. An algorithm for unsupervised learning based upon a Hebbian learning rule, which achieves the desired optimality is presented, The algorithm finds the eigenvectors of the input correlation matrix, and it is proven to converge with probability one. An implementation which can train neural networks using only local "synaptic" modification rules is described. It is shown that the algorithm is closely related to algorithms in statistics (Factor Analysis and Principal Components Analysis) and neural networks (Selfsupervised Backpropagation, or the "encoder" problem). It thus provides an explanation of certain neural network behavior in terms of classical statistical techniques. Examples of the use of a linear network for solving image coding and texture segmentation problems are presented. Also, it is shown that the algorithm can be used to find "visual receptive fields" which are qualitatively similar to those found in primate retina and visual cortex.
Texture classification by wavelet packet signatures
 IEEE Transaction PAMI
, 1993
"... This paper introduces a new approach tocharacterize textures at multiple scales. The performance of wavelet packet spaces are measured in terms of sensitivity and selectivity for the classi cation of twenty ve natural textures. Both energy and entropy metrics were computed for each wavelet packet a ..."
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Cited by 157 (3 self)
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This paper introduces a new approach tocharacterize textures at multiple scales. The performance of wavelet packet spaces are measured in terms of sensitivity and selectivity for the classi cation of twenty ve natural textures. Both energy and entropy metrics were computed for each wavelet packet and incorporated into distinct scale space representations, where each wavelet packet (channel) re ected a speci c scale and orientation sensitivity. Wavelet packet representations for twenty ve natural textures were classi ed without error by a simple twolayer network classi er. An analyzing function of large regularity (D 20) was shown to be slightly more e cient inrepresentation and discrimination than a similar function with fewer vanishing moments (D6). In addition, energy representations computed from the standard wavelet decomposition alone (17 features) provided classi cation without error for the twenty ve textures included in our study. The reliability exhibited by texture signatures based on wavelet packets analysis suggest that the multiresolution properties of such transforms are bene cial for accomplishing segmentation, classication and subtle discrimination of texture. Index Terms{Feature extraction, texture analysis, texture classi cation, wavelet transform, wavelet packet, neural networks.
Deformable Kernels for Early Vision
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1991
"... Early vision algorithms often have a first stage of linearfiltering that `extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the spac ..."
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Cited by 129 (9 self)
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Early vision algorithms often have a first stage of linearfiltering that `extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. This discretization produces anisotropies due to a loss of traslation, rotation, scalinginvariance that makes early vision algorithms less precise and more difficult to design. This need not be so: one can compute and store efficiently the response of families of linear filters defined on a continuum of orientations and scales. A technique is presented that allows (1) to compute the best approximation of a given family using linear combinations of a small number of `basis' functions; (2) to describe all finitedimensional families, i.e. the families of filters for which a finite dimensional representation is p...
Comparison of texture features based on gabor filters
 IEEE Trans. on Image Processing
"... Abstractâ€”Texture features that are based on the local power spectrum obtained by a bank of Gabor filters are compared. The features differ in the type of nonlinear postprocessing which is applied to the local power spectrum. The following features are considered: Gabor energy, complex moments, and ..."
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Cited by 102 (5 self)
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Abstractâ€”Texture features that are based on the local power spectrum obtained by a bank of Gabor filters are compared. The features differ in the type of nonlinear postprocessing which is applied to the local power spectrum. The following features are considered: Gabor energy, complex moments, and grating cell operator features. The capability of the corresponding operators to produce distinct feature vector clusters for different textures is compared using two methods: the Fisher criterion and the classification result comparison. Both methods give consistent results. The grating cell operator gives the best discrimination and segmentation results. The texture detection capabilities of the operators and their robustness to nontexture features are also compared. The grating cell operator is the only one that selectively responds only to texture and does not give false response to nontexture features such as object contours. Index Termsâ€”Classification, complex moments, discrimination,
Robust computation of optic flow in a multiscale differential framework
 International Journal of Computer Vision
, 1995
"... Abstract. We have developed a new algorithm for computing optical flow in a differential framework. The image sequence is first convolved with a set of linear, separable spatiotemporal filter kernels similar to those that have been used in other early vision problems such as texture and stereopsis. ..."
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Cited by 95 (2 self)
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Abstract. We have developed a new algorithm for computing optical flow in a differential framework. The image sequence is first convolved with a set of linear, separable spatiotemporal filter kernels similar to those that have been used in other early vision problems such as texture and stereopsis. The brightness constancy constraint can then be applied to each of the resulting images, giving us, in general, an overdetermined system of equations for the optical flow at each pixel. There are three principal sources of error: (a) stochastic error due to sensor noise (b) systematic errors in the presence of large displacements and (c) errors due to failure of the brightness constancy model. Our analysis of these errors leads us to develop an algorithm based on a robust version of total least squares. Each optical flow vector computed has an associated reliability measure which can be used in subsequent processing. The performance of the algorithm on the data set used by Barron et al. (IJCV 1994) compares favorably with other techniques. In addition to being separable, the filters used are also causal, incorporating only past time frames. The algorithm is fully parallel and has been implemented on a multiple processor machine. 1
SteerableScalable Kernels for Edge Detection and Junction Analysis
 Image and Vision Computing
, 1992
"... Families of kernels that are useful in a variety of early vision algorithms may be obtained by rotating and scaling in a continuum a `template' kernel. These multiscale multiorientation family may be approximated by linear interpolation of a discrete finite set of appropriate `basis' kernels. A sc ..."
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Cited by 79 (1 self)
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Families of kernels that are useful in a variety of early vision algorithms may be obtained by rotating and scaling in a continuum a `template' kernel. These multiscale multiorientation family may be approximated by linear interpolation of a discrete finite set of appropriate `basis' kernels. A scheme for generating such a basis together with the appropriate interpolation weights is described. Unlike previous schemes by Perona, and Simoncelli et al. it is guaranteed to generate the most parsimonious one. Additionally, it is shown how to exploit two symmetries in edgedetection kernels for reducing storage and computational costs and generating simultaneously endstop and junctiontuned filters for free.
Overcomplete steerable pyramid filters and rotation invariance
 In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
, 1994
"... A given (overcomplete) discrete oriented pyramid may be converted into a steerable pyramid by interpolation. We present a technique for deriving the optimal interpolation functions (otherwise called steering coefficients). The proposed scheme is demonstrated on a computationally efficient oriented p ..."
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Cited by 61 (4 self)
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A given (overcomplete) discrete oriented pyramid may be converted into a steerable pyramid by interpolation. We present a technique for deriving the optimal interpolation functions (otherwise called steering coefficients). The proposed scheme is demonstrated on a computationally efficient oriented pyramid, which is a variation on the Burt and Adelson pyramid. We apply the generated steerable pyramid to orientationinvarianttexture analysis to demonstrate its excellent rotational isotropy. High classification rates and precise rotation identification are demonstrated. 1