Results 1  10
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57
The Design and Use of Steerable Filters
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1991
"... Oriented filters are useful in many early vision and image processing tasks. One often needs to apply the same filter, rotated to different angles under adaptive control, or wishes to calculate the filter response at various orientations. We present an efficient architecture to synthesize filters of ..."
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Cited by 1079 (11 self)
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Oriented filters are useful in many early vision and image processing tasks. One often needs to apply the same filter, rotated to different angles under adaptive control, or wishes to calculate the filter response at various orientations. We present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters, allowing one to adaptively "steer" a filter to any orientation, and to determine analytically the filter output as a function of orientation.
Shiftable Multiscale Transforms
, 1992
"... Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavel ..."
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Cited by 559 (36 self)
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Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal, and in two dimensions, rotations of the input signal. We formalize these problems by defining a type of translation invariance that we call "shiftability". In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are specified by the sampling theorem. Shiftability may also be considered in the context of other domains, particularly orientation and scale. We explore "jointly shiftable" transforms that are simultaneously shiftable in more than one domain. Two examples of jointly shiftable transforms are designed and implemented: a onedimensional tran...
Steerable Filters and Local Analysis of Image Structure
, 1992
"... Two paradigms for visual analysis are topdown, starting from highlevel models or information about the image, and bottomup, where little is assumed about the image or objects in it. We explore a local, bottomup approach to image analysis. We develop operators to identify and classify image junct ..."
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Cited by 31 (0 self)
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Two paradigms for visual analysis are topdown, starting from highlevel models or information about the image, and bottomup, where little is assumed about the image or objects in it. We explore a local, bottomup approach to image analysis. We develop operators to identify and classify image junctions, whichcontain important visual cues for identifying occlusion, transparency, and surface bends. Like the human visual system, we begin with the application of linear filters which are oriented in all possible directions. Wedevelop an efficientway to create an oriented filter of arbitrary orientation by describing it as a linear combination of basis filters. This approach to oriented filtering, which we call steerable filters, offers advantages for analysis as well as computation. We design a variety of steerable filters, including steerable quadrature pairs, which measure local energy. We show applications of these filters in orientation and texture analysis, and image representation and enhanc...
The Gaussian Derivative model for spatialtemporal vision
 I. Cortical Model. Spatial Vision
, 2001
"... Abstract—Receptive � elds of simple cells in the primate visual cortex were well � t in the space and time domains by the Gaussian Derivative (GD) model for spatiotemporal vision. All 23 � elds in the data sample could be � t by one equation, varying only a single shape number and nine geometric tr ..."
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Cited by 30 (0 self)
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Abstract—Receptive � elds of simple cells in the primate visual cortex were well � t in the space and time domains by the Gaussian Derivative (GD) model for spatiotemporal vision. All 23 � elds in the data sample could be � t by one equation, varying only a single shape number and nine geometric transformation parameters. A differenceofoffsetGaussians (DOOG) mechanism for the GD model also � t the data well. Other models tested did not � t the data as well as or as succinctly, or failed to converge on a unique solution, indicatingoverparameterization.An ef � cient computationalalgorithm was found for the GD model which produced robust estimates of the direction and speed of moving objects in real scenes. 1.
Passive Depth From Defocus Using a Spatial Domain Approach
 In Proc. of the Intl. Conf. of Computer Vision
, 1997
"... This paper presents an algorithm for a dense computation of the difference in blur between two images. The two images are acquired by varying the intrinsic parameters of the camera. The image formation system is assumed to be passive. Estimation of depth from the blur difference is straightforward. ..."
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Cited by 13 (1 self)
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This paper presents an algorithm for a dense computation of the difference in blur between two images. The two images are acquired by varying the intrinsic parameters of the camera. The image formation system is assumed to be passive. Estimation of depth from the blur difference is straightforward. The algorithm is based on a local image decomposition technique using the Hermite polynomial basis. We show that any coefficient of the Hermite polynomial computed using the more blurred image is a function of the partial derivatives of the other image and the blur difference. Hence, the blur difference can be computed by resolving a system of equations. All computations required are local and carried out in the spatial domain. An algorithm is presented for estimation of the blur in 1D and 2D cases and its behavior is studied for constant images, step edges, line edges and junctions. The algorithm is tested using synthetic and real images. The results obtained are very encouraging. 1 Introd...
A RotationInvariant Pattern Signature
 IEEE ICIP
, 1996
"... closely related, often differing only by a linear transformation. Consider the problem of matching an observed local image intensity pattern against a set of candidate patterns. A bruteforce solution, in which one rotates the image pattern through a set of discretized orientations searching for an ..."
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Cited by 11 (1 self)
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closely related, often differing only by a linear transformation. Consider the problem of matching an observed local image intensity pattern against a set of candidate patterns. A bruteforce solution, in which one rotates the image pattern through a set of discretized orientations searching for an optimal match is inelegant, inefficient, and highly susceptible to local minima. A number of authors have taken the approach of first estimating a "dominant" orientation from the projection onto loworder basis functions (e.g., the gradient), and using this estimate to align the two patterns for comparison (e.g., [7, 14, 15, 16, 5]). This type of approach, while efficient, becomes unstable for patterns lacking a Research partially supported by an NSF CAREER grant to EPS. strongly dominant orientation. More generally, one can use the theory of algebraic invariants to construct rotationinvariant representations of image content [1, 12, 13, 14]. The theory allows one to constr
Depth From Defocus Estimation in Spatial Domain
 Computer Vision and Image Understanding
, 1999
"... This paper presents an algorithm for a dense computation of the difference in blur between two images. The two images are acquired by varying the intrinsic parameters of the camera. The image formation system is assumed to be passive. Estimation of depth from the blur difference is straightforward. ..."
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Cited by 9 (0 self)
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This paper presents an algorithm for a dense computation of the difference in blur between two images. The two images are acquired by varying the intrinsic parameters of the camera. The image formation system is assumed to be passive. Estimation of depth from the blur difference is straightforward. The algorithm is based on a local image decomposition technique using the Hermite polynomial basis. We show that any coecient of the Hermite polynomial computed using the more blurred image is a function of the partial derivatives of the other image and the blur dierence. Hence, the blur difference is computed by resolving a system of equations. The resulting estimation is dense and involves simple local operations carried out in the spatial domain. The mathematical developments underlying estimation of the blur in both 1D and 2D images are presented. The behavior of the algorithm is studied for constant images, step edges, line edges and junctions. The selection of its parameters is discussed...
ALGEBRAIC SIGNAL PROCESSING THEORY: COOLEYTUKEY TYPE ALGORITHMS FOR POLYNOMIAL TRANSFORMS BASED ON INDUCTION
"... A polynomial transform is the multiplication of an input vector x ∈ C n by a matrix Pb,α ∈ C n×n, whose (k,ℓ)th element is defined as pℓ(αk) for polynomials pℓ(x) ∈ C[x] from a list b = {p0(x),...,pn−1(x)} and sample points αk ∈ C from a list α = {α0,...,αn−1}. Such transforms find applications in ..."
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Cited by 7 (4 self)
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A polynomial transform is the multiplication of an input vector x ∈ C n by a matrix Pb,α ∈ C n×n, whose (k,ℓ)th element is defined as pℓ(αk) for polynomials pℓ(x) ∈ C[x] from a list b = {p0(x),...,pn−1(x)} and sample points αk ∈ C from a list α = {α0,...,αn−1}. Such transforms find applications in the areas of signal processing, data compression, and function interpolation. Important examples include the discrete Fourier and cosine transforms. In this paper we introduce a novel technique to derive fast algorithms for polynomial transforms. The technique uses the relationship between polynomial transforms and the representation theory of polynomial algebras. Specifically, we derive algorithms by decomposing the regular modules of these algebras as a stepwise induction. As an application, we derive novel O(nlogn) generalradix algorithms for the discrete Fourier transform and the discrete cosine transform of type 4.
Projection Filtering in Image Processing
"... In this paper we shall consider the new projection scheme of local image processing of the visual information. It is based on an expansion into series of eigenfunctions of the Fourier transform. This scheme can be used for compression of images and any kind other media data, their filtration, tracin ..."
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Cited by 6 (1 self)
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In this paper we shall consider the new projection scheme of local image processing of the visual information. It is based on an expansion into series of eigenfunctions of the Fourier transform. This scheme can be used for compression of images and any kind other media data, their filtration, tracing of outlines, definition of structures and properties of objects.
Numerical projection method for inverse Fourier transform and its application
 Numer. Funct. Anal. Optim
, 2000
"... Numerical projection method of the Fourier transform inversion from data given on a finite interval is proposed. It is based on an expansion of the solution into a series of eigenfunctions of the Fourier transform. The number of terms of the expansion depends on the length of the data interval. Conv ..."
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Cited by 5 (3 self)
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Numerical projection method of the Fourier transform inversion from data given on a finite interval is proposed. It is based on an expansion of the solution into a series of eigenfunctions of the Fourier transform. The number of terms of the expansion depends on the length of the data interval. Convergence of the solution of the method is proved. The projection method for the case of the sine Fourier transform and the set of the odd Hermite functions being its eigenfunctions are examined and applied to numerical Fourier filtering.