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Robust and efficient FourierMellin transform approximations for graylevel image reconstruction and complete invariant description
"... This paper addresses the graylevel image representation ability of the FourierMellin Transform (FMT) for pattern recognition, reconstruction and image database retrieval. The main practical difficulty of the FMT lies in the accuracy and efficiency of its numerical approximation and we propose thre ..."
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Cited by 29 (3 self)
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This paper addresses the graylevel image representation ability of the FourierMellin Transform (FMT) for pattern recognition, reconstruction and image database retrieval. The main practical difficulty of the FMT lies in the accuracy and efficiency of its numerical approximation and we propose three estimations of its analytical extension. Comparison of these approximations is performed from discrete and finiteextent sets of FourierMellin harmonics by means of experiments in: (i) image reconstruction via both visual inspection and the computation of a reconstruction error; and (ii) pattern recognition and discrimination by using a complete and convergent set of features invariant under planar similarities. Experimental results
Shape Analysis and Symmetry Detection In GrayLevel Objects using the analytical FourierMellin . . .
, 2003
"... The analytical FourierMellin transform is used in order to assess motion parameters between graylevel objects having the same shape with distinct scale and orientation. From results on commutative harmonic analysis, a functional is constructed in which the location of the minimum gives an estimati ..."
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Cited by 18 (0 self)
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The analytical FourierMellin transform is used in order to assess motion parameters between graylevel objects having the same shape with distinct scale and orientation. From results on commutative harmonic analysis, a functional is constructed in which the location of the minimum gives an estimation of the size and orientation parameters. Furthermore, when the set of geometrical transformations is restricted to the compact rotation group, we show that this minimum is exactly the Hausdorff distance between shapes represented in the FourierMellin domain. This result is used for the detection and the estimation of both all rotation and reflection symmetric in objects.
Twists  An Operational Representation of Shape
"... We give a contribution to the representation problem of freeform curves and surfaces. Our proposal is an operational or kinematic approach based on the Lie group SE(3). While in Euclidean space the modelling of shape as an orbit of a point under the action of SE(3) is limited, we are embedding our ..."
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We give a contribution to the representation problem of freeform curves and surfaces. Our proposal is an operational or kinematic approach based on the Lie group SE(3). While in Euclidean space the modelling of shape as an orbit of a point under the action of SE(3) is limited, we are embedding our problem into the conformal geometric algebra R4,1 of the Euclidean space R 3. This embedding results in a number of advantages which makes the proposed method a universal and flexible one with respect to applications. It makes possible the robust and fast estimation of the pose of 3D objects from incomplete and noisy image data. Especially advantagous is the equivalence of the proposed shape model to that of the Fourier representations.
Geometric Analysis of the Conformal Camera for IntermediateLevel Vision and Perisaccadic Perception
, 2009
"... A binocular system developed by the author in terms of projective Fourier transform (PFT) of the conformal camera, which numerically integrates the head, eyes, and visual cortex, is used to process visual information during saccadic eye movements. Although we make three saccades per second at the ey ..."
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A binocular system developed by the author in terms of projective Fourier transform (PFT) of the conformal camera, which numerically integrates the head, eyes, and visual cortex, is used to process visual information during saccadic eye movements. Although we make three saccades per second at the eyeball’s maximum speed of 700 deg/sec, our visual system accounts for these incisive eye movements to produce a stable percept of the world. This visual constancy is maintained by neuronal receptive field shifts in various retinotopically organized cortical areas prior to saccade onset, giving the brain access to visual information from the saccade’s target before the eyes ’ arrival. It integrates visual information acquisition across saccades. Our modeling utilizes basic properties of PFT. First, PFT is computable by FFT in complex logarithmic coordinates that approximate the retinotopy. Second, a translation in retinotopic (logarithmic) coordinates, modeled by the shift property of the Fourier transform, remaps the presaccadic scene into a postsaccadic reference frame. It also accounts for the perisaccadic mislocalization observed by human subjects in laboratory experiments. Because our modeling involves crossdisciplinary areas of conformal geometry, abstract and computational harmonic analysis, computational vision, and visual neuroscience, we include the corresponding background material and elucidate how these different areas interwove in our modeling of primate perception. In particular, we present the physiological and behavioral facts underlying the neural processes related to our modeling. We also emphasize the conformal camera’s geometry and discuss how it is uniquely useful in the intermediatelevel vision computational aspects of natural scene understanding.
The Journal of Fourier Analysis and Applications "Online First" Geometric Fourier Analysis for Computational Vision
"... ABSTRACT. Projective Fourier analysis—geometric Fourier analysis of the group SL(2,C), the group identified in the conformal camera that provides image perspective transformations—is discussed in the framework of representation theory of semisimple Lie groups. The compact model of projective Fourier ..."
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ABSTRACT. Projective Fourier analysis—geometric Fourier analysis of the group SL(2,C), the group identified in the conformal camera that provides image perspective transformations—is discussed in the framework of representation theory of semisimple Lie groups. The compact model of projective Fourier analysis is constructed, complementing the noncompact model proposed before. Detailed mathematical formulation of both models is presented. It is demonstrated that the projective Fourier analysis provides the data model for efficient perspectively covariant digital image representation well adapted to the retinocortical mapping of biological visual system, and therefore, explicitly designed for the foveated sensors of a silicon retina, the use of which in active vision systems is presently limited due to the lack of such a model. 1.
Corresponding author, Département Image et Traitement de l’Information,
, 2008
"... approximations for graylevel image reconstruction and complete invariant description ..."
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approximations for graylevel image reconstruction and complete invariant description