related bibliography on edge detection

• David Marr, Ellen Hildreth. Theory of edge detection. Proceedings of the Royal Society of London. Series B, Biological Sciences, 207:187-217, 1980 abstract
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• Peter J. Burt, Edward H. Adelson. The Laplacian Pyramid as a compact image code. IEEE Transactions on Communications, COM-31,4:532--40, 1983 abstract
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• J. Canny. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 8:679-98, 1986 abstract
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• Rachid Deriche. Using Canny's criteria to derive a recusively implemented optimal edge detector. International Journal of Computer Vision, :167-87, 1987 abstract
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• Rachid Deriche. Fast Algorithms for Low-Level Vision. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 1(12):78--8, 1990 abstract
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• S. Castan, J. Zhao, J. Shen. Optimal Filter for Edge Detection Methods and Results. In In Proceedings of the First European Conference on Computer Vision (Eccv), pages 13-7. 1990 abstract
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• Stéphane Mallat, Sifen Zhong. Wavelet Transform Maxima and Multiscale Edge. In Wavelets and Their Applications, pages 67--104. Jones and Bartlett Publishers, 1992 abstract
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• Stéphane Mallat, Sifen Zhong. Characterization of Signals from Multiscale Edges. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 14(7):710--32, 1992 abstract
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• Anthony J. Bell, Terrence J. Sejnowski. The `independent components' of natural scenes are edge filters. Vision Research, 37(23):3327--38, 1997 abstract
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• K. R. Popper. All Life Is Problem Solving. Routledge, London, 1999.
• Charles Poynton. Frequently Asked Questions about Gamma. 1999.
• Antonio Turiel, Néstor Parga. The multifractal structure of contrast changes in natural images: from sharp edges to textures.. Neural Computation, 12:763--93, 2000 abstract
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• Wilson S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly. Edge co-occurance in natural images predicts contour grouping performance.. Vision Research, 41(6):711-24, 2001 abstract
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• Guillaume S. Masson, L.S. Stone. From following edges to pursuing objects, URL . Journal of Neurophysiology, 88(5):2869--73, 2002 abstract
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• Antonio Turiel, Angela del Pozo. Reconstructing images from their most singular fractal manifold. IEEE Transactions in Image Processing, 11(4):345--50, 2002 abstract
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• Jean Petitot. The neurogeometry of pinwheels as a sub-Riemannian contact structure, URL . Journal of Physiology (Paris), 97(2-3):265--309, 2003 abstract
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• Sylvain Fischer, Rafael Redondo, Laurent Perrinet, Gabriel Crist\'obal. Efficient representation of natural images using local cooperation. In Perception, pages 241. 2005 abstract
  Low-level perceptual computations may be understood in terms of efficient codes (Simoncelli and Olshausen, 2001, Annual Review of Neuroscience 24 1193-216). Following this argument, we explore models of representation for natural static images as a way to understand the processing of information in the primary visual cortex. This representation is here based on a generative linear model of the synthesis of images using an over-complete multi-resolution dictionary of edges. This transform is implemented using log-Gabor filters and permits an exact reconstruction of any image. However, this linear representation is redundant and since to any image may correspond different representations, we explore more efficient representations of the image. The problem is stated as an ill-posed inverse problem and we compare first different known strategies by computing the efficiency of the solutions given by Matching Pursuit (Perrinet, 2004, IEEE Trans. Neural Networks 15 1164-75) and sparse edge coding (Fischer, in press, Trans. Image Processing) with classical representation methods such as JPEG. This comparison allows us to provide a synthesized approach using a probabilistic representation which would progressively construct the neural representation by using lateral cooperations. We propose an algorithm which dynamically diffuses information to correlated filters so as to yield a progressively disambiguated representation. This approach takes advantage of the computational properties of spiking neurons such as Integrate-and-Fire neurons and provides an efficient yet simple model for the representation of natural images. This representation is directly linked with the edge content of natural images and we show applications of this method to edge extraction, denoising and compression. We also show that this dynamical approach fits with neuro-physiological observations and may explain the non-linear interactions between neighboring neurons which may be observed in the cortex.
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• Sylvain Fischer, Rafael Redondo, Laurent Perrinet, Gabriel Crist\'obal. Sparse Gabor wavelets by local operations. In Proceedings SPIE, pages 75--86. 2005 abstract
  Efficient sparse coding of overcomplete transforms remains still anopen problem. Different methods have been proposed in theliterature, but most of them are limited by a heavy computationalcost and by difficulties to find the optimal solutions. We proposehere an algorithm suitable for Gabor wavelets and based onbiological models. It is composed by local operations betweenneighboring transform coefficients and achieves a sparserepresentation with a relatively low computational cost. Used with achain coder, this sparse Gabor wavelet transform is suitable forimage compression but is also of interest also for otherapplications, in particular for edge and contour extraction andimage denoising.
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• Rafael Redondo, Sylvain Fischer, Laurent Perrinet, Gabriel Crist\'obal. Modeling of simple cells through a sparse overcomplete gabor wavelet representation based on local inhibition and facilitation. In Perception, pages 238. 2005 abstract
  We present a biologically plausible model of simple cortical cells as 1) a linear transform representing edges and 2) a non-linear iterative stage of inhibition and facilitation between neighboring coefficients. The linear transform is a complex log-Gabor wavelet transform which is overcomplete (i.e. there are more coefficients than pixels in the image) and has exact reconstruction. The inhibition consists in diminishing down the coefficients which are not at a local-maxima along the direction normal to the edge filter orientation, whereas the facilitation enhances the collinear and co-aligned local-maximum coefficients. At each iteration and after the inhibition and facilitation stages, the reconstructed error is subtracted in the transform domain for keeping an exact reconstruction. Such process concentrates the signal energy on a few coefficients situated along the edges of the objects, yielding a sparse representation. The rationale for such procedure is: (1) th e overcompleteness offers flexibility for activity reassignment; (2) images can be coded by sparse Gabor coefficients located on object edges; (3) image contours produce aligned and collinear local-maxima in the transform domain; (4) the inhibition/facilitation processes are able to extract the contours. The sparse Gabor coefficients are mostly connected each other and located along object contours. Such layout makes chain coding suitable for compression purposes. Specially adapted to Gabor wavelets features, our chain coding represents every chain by its end-points (head and tail) and the elementary movements necessary to walk along the chain from head to tail. Moreover it predicts the module and phase of each Gabor coefficient according to the previous chain coefficient. As a result, redundancy of the transform domain is further reduced. Used for compression, the scheme limits particularly the high-frequency artifacts. The model performs also efficiently in tasks the Human Visual System is supposed to deal with, as for instance edge extraction and image denoising.
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• Sylvain Fischer, Gabriel Crist\'obal, Rafael Redondo. Sparse Overcomplete Gabor Wavelet Representation Based on Local Competitions. IEEE Transactions in Image Processing, 15(2):265, 2006 abstract
  Gabor representations present a number of interesting properties despite the fact that the basis functions are non orthogonal and provide an overcomplete representation or a non-exact reconstruction. Overcompleteness involves an expansion of the number of coeficients in the transform domain and induces a redundancy that can be further reduced through computational costly iterative algorithms like Matching Pursuit. Here a biologically plausible algorithm based on competitions between neighboring coeficients is employed for representing adaptively any source image by a selected subset of Gabor functions. This scheme involves a sharper edge localization and a signiicant reduction of the information redundancy while at the same time the reconstruction quality is preserved. The method is characterized by its biological plausibility and promising results, but it still requires a more in depth theoretical analysis for completing its validation.
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• Laurent Perrinet, Frédéric V. Barthélemy, Guillaume S. Masson. Input-output transformation in the visuo-oculomotor loop: modeling the ocular following response to center-surround stimulation in a probabilistic framework. In 1ère conférence francophone NEUROsciences COMPutationnelles - NeuroComp, 2006 abstract
  The quality of the representation of an object's motion is limited by the noise in the sensory input as well as by an intrinsic ambiguity due to the spatial limi- tation of the visual motion analyzers (aperture prob- lem). Perceptual and oculomotor data demonstrate that motion processing of extended ob jects is initially dominated by the local 1D motion cues orthogonal to the ob ject's edges, whereas 2D information takes pro- gressively over and leads to the final correct represen- tation of global motion. A Bayesian framework ac- counting for the sensory noise and general expectancies for ob ject velocities has proven successful in explaining several experimental findings concerning early motion processing [1, 2, 3]. However, a complete functional model, encompassing the dynamical evolution of ob- ject motion perception is still lacking. Here we outline several experimental observations concerning human smooth pursuit of moving ob jects and more particu- larly the time course of its initiation phase. In addi- tion, we propose a recursive extension of the Bayesian model, motivated and constrained by our oculomotor data, to describe the dynamical integration of 1D and 2D motion information.
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• Sylvain Fischer, Rafael Redondo, Laurent Perrinet, Gabriel Crist\'obal. Sparse approximation of images inspired from the functional architecture of the primary visual areas, URL . EURASIP Journal on Advances in Signal Processing, 2007(1):122, 2007 abstract
  Abstract--- Meanwhile biorthogonal wavelets got a very popu- lar image processing tool, alternative multiresolution transforms have been proposed for solving some of their drawbacks, namely the poor selectivity in orientation and the lack of translation in- variance due to the aliasing between subbands. These transforms are generally overcomplete and consequently offer huge degrees of freedom in their design. At the same time their optimization get a challenging task. We proposed here a log-Gabor wavelet transform gathering the excellent mathematical properties of the Gabor functions with a carefully construction to maintain the properties of the filters and to permit exact reconstruction. Two major improvements are proposed: first the highest frequency bands are covered by narrowly localized oriented filters. And second, all the frequency bands including the highest and lowest frequencies are uniformly covered so as exact reconstruction is achieved using the same filters in both the direct and the inverse transforms (which means that the transform is self-invertible). The transform is optimized not only mathematically but it also follows as much as possible the knowledge on the receptive field of the simple cells of the Primary Visual Cortex (V1) of primates and on the statistics of natural images. Compared to the state of the art, the log-Gabor wavelets show excellent behavior in their ability to segregate the image information (e.g. the contrast edges) from incoherent Gaussian noise by hard thresholding and to code the image features through a reduced set of coefficients with large magnitude. Such characteristics make the transform a promising tool for general image processing tasks.
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• Sylvain Fischer, Filip Sroubek, Laurent Perrinet, Rafael Redondo, Gabriel Crist\'obal. Self-invertible 2D log-Gabor wavelets. International Journal of Computer Vision, 2007 abstract
  Abstract--- Meanwhile biorthogonal wavelets got a very popu- lar image processing tool, alternative multiresolution transforms have been proposed for solving some of their drawbacks, namely the poor selectivity in orientation and the lack of translation in- variance due to the aliasing between subbands. These transforms are generally overcomplete and consequently offer huge degrees of freedom in their design. At the same time their optimization get a challenging task. We proposed here a log-Gabor wavelet transform gathering the excellent mathematical properties of the Gabor functions with a carefully construction to maintain the properties of the filters and to permit exact reconstruction. Two major improvements are proposed: first the highest frequency bands are covered by narrowly localized oriented filters. And second, all the frequency bands including the highest and lowest frequencies are uniformly covered so as exact reconstruction is achieved using the same filters in both the direct and the inverse transforms (which means that the transform is self-invertible). The transform is optimized not only mathematically but it also follows as much as possible the knowledge on the receptive field of the simple cells of the Primary Visual Cortex (V1) of primates and on the statistics of natural images. Compared to the state of the art, the log-Gabor wavelets show excellent behavior in their ability to segregate the image information (e.g. the contrast edges) from incoherent Gaussian noise by hard thresholding and to code the image features through a reduced set of coefficients with large magnitude. Such characteristics make the transform a promising tool for general image processing tasks.
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