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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 843 (12 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.
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 131 (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...
Detecting And Localizing Edges Composed Of Steps, Peaks And Roofs
 In Proc. 3rd Intl. Conf. Computer Vision
, 1991
"... It is well known that the projection of depth or orientation discontinuities in a physical scene results in im age intensity edges which are not ideal step edges but are more typically a combination of steps, peak and roof profiles. However most edge detection schemes ignore the composite nature of ..."
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Cited by 82 (18 self)
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It is well known that the projection of depth or orientation discontinuities in a physical scene results in im age intensity edges which are not ideal step edges but are more typically a combination of steps, peak and roof profiles. However most edge detection schemes ignore the composite nature of these edges, resulting in systematic errors in detection and localization. We address the problem of detecting and localizing these edges, while at the same time also solving the problem of false responses in smoothly shaded regions with constant gradient of the image brightness. We show that a class of nonlinear filters, known as quadratic filters, are appropriate for this task, while linear filters are not. A series of performance criteria are derived for characterizing the $NR, localization and multiple responses of these filters in a manner analogous to Canny's criteria for linear filters. A twodimensional version of the approach is developed which has the property of being able to represent multiple edges at the same location and determine the orientation of each to any desired precision. This permits junctions to be localized without rounding. Ezperimental results are presented.
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 80 (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.
Detecting Curvilinear Structure in Images
 University of California at Berkeley
, 1991
"... Humans have a well developed ability to detect curvilinear structure in noisy images. Good algorithms for performing this process would be very useful in machine vision for image segmentation and object recognition. Previous approaches to this problem such as those due to Parent and Zucker and Sha’s ..."
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Cited by 8 (0 self)
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Humans have a well developed ability to detect curvilinear structure in noisy images. Good algorithms for performing this process would be very useful in machine vision for image segmentation and object recognition. Previous approaches to this problem such as those due to Parent and Zucker and Sha’shua and Ullman have been based on relaxation. We have developed a simple feedforward and parallel approach to this problem based on the idea of developing filters tuned to local oriented circular arcs. This provides a natural second order generalization of the idea of directional operators popular for edge detection. Curve detection can then be done by methods very similar to those used for edge detection. Experimental results are shown on both synthetic and natural images. We also review data from an experiment investigating human preattentive line segregation and present predictions from our model that agree with this data. „�™���™— � ‚���� � …gfGgƒh WIGTIWD g������ � ƒ™ � ��™ �
Figure 6: The arrangement of the images is the same as in Figure 5. 14
"... of the resulting images we computed C(x; y; 0 ; 0), and C(x; y; 90 ; 0) using oe of 6.5 pixels. To measure the errors predicted by our algorithm we used the negative of the ratio of the total response in the central vertical strip of C(x; y; 90 ; 0) to the total response in the central hor ..."
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of the resulting images we computed C(x; y; 0 ; 0), and C(x; y; 90 ; 0) using oe of 6.5 pixels. To measure the errors predicted by our algorithm we used the negative of the ratio of the total response in the central vertical strip of C(x; y; 90 ; 0) to the total response in the central horizontal strip of C(x; y; 0 ; 0). The strips were 8 pixels wide. The resulting predictions are plotted in Figures 8b. Note, that the algorithm predicts the trend evident from the psychophysical data, where the lines made of collinear blobs or bars are detected more reliably then lines made of orthogonal elements. 15 Figure 7: The stimuli for experiment 1. The target line is vertical. In the first and second columns are the collinear bars and blobs, respectively. In the third and forth columns are the corresponding orthogonal elements. Aspect ratios are, from top to bottom, 1,1.8, and 2.3. 1.00 bars colinear blobs colinear Aspect ratio Long/Short Axis 1.8 2.3 blobs orthogonal bars
LIDSP2039 Deformable kernels for early vision
, 1991
"... perona @ verona. caltech. edu 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 ..."
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perona @ verona. caltech. edu 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 possible with no error. The technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions. Experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multiscale 2D edgedetection kernels. The implementation issues are also discussed.