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## Edge Detection and Ridge Detection with Automatic Scale Selection (1996)

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Venue: | CVPR'96 |

Citations: | 347 - 24 self |

### Citations

4694 | A Computational Approach to Edge Detection.”
- Canny
- 1986
(Show Context)
Citation Context ...oduct of the variances of the filter in the spatial and the Fourier domains. 1 Other early techniques with a multi-scale character were presented by (Rosenfeld and Thurston 1971) and by (Marr 1976). (=-=Canny 1986) consider-=-ed the problem of determining an "optimal smoothing filter " of finite support for detecting step edges. The methodology was to maximize a certain performance measure constituting a trade-o#... |

2700 | Marching Cubes: A high resolution 3D surface construction algorithm.
- Lorensen, Harvey
- 1987
(Show Context)
Citation Context ...g surfaces, the next step is to construct a polygon approximation of the intersection of these surfaces. In this implementation, we traverse all voxels in a way closely related to the marching cubes (=-=Lorensen and Cline 1987-=-) and the marching lines (Thirion and Gourdon 1993) algorithms. For each voxel, a test is made if there the intersection of iso-surfaces passes through that voxel. Then, on top of this construction, a... |

1893 | Scale-space and edge detection using anisotropic diffusion,
- Perona, Malik
- 1990
(Show Context)
Citation Context ...been given large attention during recent years, is the replacement of the linear smoothing operation by a non-linear smoothing step, with the goal of avoiding smoothing across object boundaries, see (=-=Perona and Malik 1990-=-; Saint-Marc et al. 1991; Nitzberg and Shiota 1992; Haar Romeny 1994) for examples. A trade-o# problem, which is common for all these edge detection schemes, and, in fact, arises for any multi-scale f... |

1290 | Theory of edge detection,”
- Marr, Hildreth
- 1980
(Show Context)
Citation Context ...Poggio 1980) motivated the need for linear filtering as a pre-processing step to di#erentiation, in order to regularize ill-posed di#erentiation into well-posed operators. The Marr-Hildreth operator (=-=Marr and Hildreth 1980-=-) was motivated by the rotational symmetry of the Laplacian operator and the special property of the Gaussian kernel as being the only real function that minimizes the product of the variances of the ... |

861 |
The Structure of Images,"
- Koenderink
- 1984
(Show Context)
Citation Context ...er computing descriptors from image data concerns what image operators to use. A systematic approach that has been developed for dealing with this problem is provided scale-space theory (Witkin 1983; =-=Koenderink 1984-=-; Yuille and Poggio 1986; Lindeberg 1990, 1994c; Florack et al. 1992). It focuses on the basic fact that image structures, like objects in the world, exist as meaningful entities over certain ranges o... |

725 | Feature detection with automatic scale selection.
- Lindeberg
- 1998
(Show Context)
Citation Context ...e invariant to size changes. This property is a direct consequency of the fact that the #-normalized scale-space derivatives transform according to power laws (see section 4.1 in the companion paper (=-=Lindeberg 1996-=-)), and that these saliency measures are self-similar functions of homogenous di#erential expressions. 12 With reference to the invariance properties discussed in the previous footnote, it is worth no... |

678 |
Characterization of signals from multiscale edges,
- Mallat, Zhong
- 1992
(Show Context)
Citation Context ...ch extends the notion of non-maximum suppression to a scale-space representation, and unifies this concept with several of the aims of diffuseness estimation schemes such as (Zhang and Bergholm 1993; =-=Mallat and Zhong 1992-=-). Concerning the ridge detection problem, the same type of framework captures several of the ideas behind the works in (Pizer et al. 1994; Eberly et al. 1994; Koller et al. 1995), and is based on loc... |

674 |
Scale-space filtering,
- Witkin
- 1983
(Show Context)
Citation Context ...arises whenever computing descriptors from image data concerns what image operators to use. A systematic approach that has been developed for dealing with this problem is provided scale-space theory (=-=Witkin 1983-=-; Koenderink 1984; Yuille and Poggio 1986; Lindeberg 1990, 1994c; Florack et al. 1992). It focuses on the basic fact that image structures, like objects in the world, exist as meaningful entities over... |

628 | Scale-Space Theory in Computer Vision.
- Lindeberg
- 1994
(Show Context)
Citation Context ...ent magnitude assumes a maximum in the gradient direction, and can be given either an algorithmic or differential geometric definition. In this way, edges can be detected at any scale in scale-space (=-=Lindeberg 1994-=-). The subject of this article is to extend the abovementioned ideas to include the scale dimension already in the edge definition, to simultaneously allow for automatic determination of scale levels ... |

333 |
Machine Perception of Three-Dimensional Solids.
- Roberts
- 1965
(Show Context)
Citation Context ...s focused on the detection of points at which the gradient magnitude is high. Derivative approximations were computed either from the pixels directly, using operators such as Robert's cross operator (=-=Roberts 1965-=-), the Sobel operator (Pingle 1969) and the Prewitt operator (Prewitt 1970), or from local least-squares fitting (Haralick 1984). An important step was then taken by the introduction of multi-scale te... |

290 | Using Canny’s criteria to derive a recursively implemented optimal edge detector, - Deriche - 1987 |

254 |
Catastrophe theory and its applications.
- Poston, Stewart
- 1978
(Show Context)
Citation Context ...ned from the following polynomial 8 L v (x; t) = L x (x; t) = x 3 + 3 x (t - t b ), (36) which represents the canonical type of singularity in a one-parameter family of functions,sthe fold unfolding (=-=Poston and Stewart 1978-=-), and also has the attractive property that it satisfies the di#usion equation (here, t b denotes the bifurcation scale). Di#erentiation gives L vv (x; t) = L xx (x; t) = 3(x 2 + t - t b ) = 0, (37) ... |

244 | On edge detection.
- Torre, Poggio
- 1986
(Show Context)
Citation Context ...l operator (Pingle 1969) and the Prewitt operator (Prewitt 1970), or from local least-squares fitting (Haralick 1984). An important step was then taken by the introduction of multi-scale techniques. (=-=Torre and Poggio 1980-=-) motivated the need for linear filtering as a pre-processing step to di#erentiation, in order to regularize ill-posed di#erentiation into well-posed operators. The Marr-Hildreth operator (Marr and Hi... |

202 | Digital Step Edges from Zero Crossing of the Second Directional Derivatives”,
- Haralick
- 1984
(Show Context)
Citation Context ...rom the pixels directly, using operators such as Robert's cross operator (Roberts 1965), the Sobel operator (Pingle 1969) and the Prewitt operator (Prewitt 1970), or from local least-squares fitting (=-=Haralick 1984-=-). An important step was then taken by the introduction of multi-scale techniques. (Torre and Poggio 1980) motivated the need for linear filtering as a pre-processing step to di#erentiation, in order ... |

189 | Detecting salient blob-like image structures and their scales with a scale-space primal sketch - A method for focus-of-attention,
- Lindeberg
- 1993
(Show Context)
Citation Context ...of the notion of nonmaximum suppression, with the scale dimension included already in the edge definition. This approach builds upon previous work on feature detection with automatic scale selection (=-=Lindeberg 1993-=-c, 1994a), based on the idea that in the absence of further evidence, scale levels for feature detection can be selected from the scales at which normalized measures of feature strength assumes local ... |

181 | Scaling theorems for zero crossings,
- Yuille, Poggio
- 1986
(Show Context)
Citation Context ...riptors from image data concerns what image operators to use. A systematic approach that has been developed for dealing with this problem is provided scale-space theory (Witkin 1983; Koenderink 1984; =-=Yuille and Poggio 1986-=-; Lindeberg 1990, 1994c; Florack et al. 1992). It focuses on the basic fact that image structures, like objects in the world, exist as meaningful entities over certain ranges of scale, and that one, i... |

167 | Scale-space theory: A basic tool for analysing structures at different scales. - Lindeberg - 1994 |

159 | Hierarchic voronoi skeletons.
- Ogniewicz, Kubler
- 1995
(Show Context)
Citation Context ... distance transforms (Arcelli and Baja 1992). It is, however, well-known that features extracted in this way can be highly sensitive to small perturbations of the boundary. To reduce these problems, (=-=Ogniewicz and Kubler 1995-=-) proposed a hierarchical skeleton concept. Alternatively, this sensitivity can be reduced by grey-level based multi-scale techniques. In this section, we shall show how the framework for edge detecti... |

151 |
Early processing of visual information,”
- Marr
- 1976
(Show Context)
Citation Context ...imizes the product of the variances of the filter in the spatial and the Fourier domains. 1 Other early techniques with a multi-scale character were presented by (Rosenfeld and Thurston 1971) and by (=-=Marr 1976). (Canny -=-1986) considered the problem of determining an "optimal smoothing filter " of finite support for detecting step edges. The methodology was to maximize a certain performance measure constitut... |

140 |
Edge Focusing,"
- Bergholm
- 1987
(Show Context)
Citation Context ...e poor localization. A smaller amount of smoothing, on the other hand, can be expected to improve the localization properties at the cost of a lower signal-tonoise ratio. To circumvent this problem, (=-=Bergholm 1987-=-) proposed to detect edges at coarse scales, and to follow these to finer scales using edge focusing. He did, however, not present any method for determining the scale level for the detection step, or... |

134 | Scale-space for discrete signals,
- Lindeberg
- 1990
(Show Context)
Citation Context ...concerns what image operators to use. A systematic approach that has been developed for dealing with this problem is provided scale-space theory (Witkin 1983; Koenderink 1984; Yuille and Poggio 1986; =-=Lindeberg 1990-=-, 1994c; Florack et al. 1992). It focuses on the basic fact that image structures, like objects in the world, exist as meaningful entities over certain ranges of scale, and that one, in general, canno... |

128 |
Object Enhancement And Extraction,
- Prewitt
- 1970
(Show Context)
Citation Context ...gh. Derivative approximations were computed either from the pixels directly, using operators such as Robert's cross operator (Roberts 1965), the Sobel operator (Pingle 1969) and the Prewitt operator (=-=Prewitt 1970-=-), or from local least-squares fitting (Haralick 1984). An important step was then taken by the introduction of multi-scale techniques. (Torre and Poggio 1980) motivated the need for linear filtering ... |

124 |
Edge and curve detection for visual scene analysis,”
- Rosenfeld, Thurston
- 2011
(Show Context)
Citation Context ...being the only real function that minimizes the product of the variances of the filter in the spatial and the Fourier domains. 1 Other early techniques with a multi-scale character were presented by (=-=Rosenfeld and Thurston 1971) and by (-=-Marr 1976). (Canny 1986) considered the problem of determining an "optimal smoothing filter " of finite support for detecting step edges. The methodology was to maximize a certain performanc... |

123 |
Adaptive Smoothing: A General Tool for Early Vision”,
- Saint-Marc, Chen, et al.
- 1991
(Show Context)
Citation Context ...ion during recent years, is the replacement of the linear smoothing operation by a non-linear smoothing step, with the goal of avoiding smoothing across object boundaries, see (Perona and Malik 1990; =-=Saint-Marc et al. 1991-=-; Nitzberg and Shiota 1992; Haar Romeny 1994) for examples. A trade-o# problem, which is common for all these edge detection schemes, and, in fact, arises for any multi-scale feature detector, concern... |

116 | Scale and the differential structure of images.
- Florack, Romeny, et al.
- 1992
(Show Context)
Citation Context ...cture. 2 Principle for scale selection The scale-space representation L of a given signal f is obtained by convolving f by Gaussian kernels g of various widths t = oe 2 (Witkin 1983, Koenderink 1984, =-=Florack et al. 1992-=-, Lindeberg 1994). From this representation, a scale-space derivative is defined by L x ff y fi (\Delta; t) = @ x ff y fi (g(\Delta; t)sf) = g x ff y fi (\Delta; t)sf: The output from these operators ... |

113 |
Ridges for image analysis.
- Eberly, Gardner, et al.
- 1994
(Show Context)
Citation Context ... a measure of edge strength from each edge point and then detecting peaks in the measure of "medialness" so obtained. A more extensive discussion of di#erent types of ridge detectors is pres=-=ented by (Eberly et al. 1994-=-), including extensions to higher dimensions. Related applications of similar ideas to medical images have been presented by (Gri#n et al. 1992; Monga et al. 1994; Koller et al. 1995). 15 A more exten... |

111 | On detecting edges. - Nalwa, Binford - 1986 |

107 | A "A Representation for Shape Based on Peaks & Ridges in the Difference of Low-Pass Transform," - Crowley, Parker - 1984 |

106 | Multiscale detection of curvilinear structures in 2D and 3D image data
- Koller, Gerig, et al.
- 1995
(Show Context)
Citation Context ... is presented by (Eberly et al. 1994), including extensions to higher dimensions. Related applications of similar ideas to medical images have been presented by (Gri#n et al. 1992; Monga et al. 1994; =-=Koller et al. 1995). 15 A mo-=-re extensive summary and discussion is given in section 7.1. Edge detection and ridge detection with automatic scale selection 23 For binary data, the related notion of "skeletons" can be de... |

101 |
Scale-Space Theory in Computer Vision. The Kluwer
- Lindeberg
- 1994
(Show Context)
Citation Context ...sponds to the maximum absolute value of the principal curvature. This idea, which goes back to (Saint-Venant 1852), is closely related to the approaches in (Haralick 1983; Eberly et al. 1994). 16 In (=-=Lindeberg 1994-=-b) it is shown that in terms of the (u, v)-system described in section 4.1, this condition can for non-degenerate L equivalently be written # L uv = 0, L 2 uu - L 2 vv > 0, (48) where the sign of L uu... |

101 | Nonlinear image filtering with edge and corner enhancement. - Nitzberg, Shiota - 1992 |

82 | Object representation by cores: Identifying and representing primitive spatial regions
- Burbeck, Pizer
- 1995
(Show Context)
Citation Context ...re can be seen as a refined version of such a descriptor, which in addition provides an approximate symmetry axis of the candidate object. Psychophysical support for this idea have been presented by (=-=Burbeck and Pizer 1995-=-). When to define ridges from intensity data, there are several possible approaches. In topography, a ridge is defined as a separator between regions from which water flows in di#erent directions (to ... |

73 | Generic neighborhood operators", - Koenderink, Doorn - 1992 |

60 |
Multiresolution analysis of ridges and valleys in grey-scale images,
- Gauch, Pizer
- 1993
(Show Context)
Citation Context ...4), who considered directional maxima in bandpass filtered images. During more recent years, the ridge detection problem has been intensively studied by Pizer and his co-workers (Pizer et al. 1994). (=-=Gauch and Pizer 1993) define r-=-idges from topographical watersheds computed in a scale-space representation of the image data. (Morse et al. 1994) compute "core" descriptors in a multi-scale fashion by propagating a measu... |

60 |
Ridges and valleys in digital images.
- Haralick
- 1983
(Show Context)
Citation Context ...er, lead to a large number of confusions. A historic account of this development is given by (Koenderink and van Doorn 1994). In computer vision, early approaches to ridge detection were proposed by (=-=Haralick 1983-=-), who defined bright (dark) ridges as points for which the main principal curvature assumes a maximum (minimum) in the main principal curvature direction, and by (Crowley and Parker 1984), who consid... |

53 | On scale selection for differential operators.
- Lindeberg
- 1993
(Show Context)
Citation Context ...ture detector, however, concerns at what scales the image features should be extracted, and what image features should be regarded as significant. Early work addressing this problem was presented in (=-=Lindeberg 1993-=-a) for blob-like image structures. Then, in (Lindeberg 1993b, 1994) an extension was presented to other aspects of image structure. A general heuristic principle was proposed stating that local maxima... |

51 |
Optimal edge detectors for ramp edges”,
- Petrou
- 1991
(Show Context)
Citation Context ...sm for distinguishing "false" from "true" edges. 2 In two dimensions, however, such recursive filters may be strongly biased to the orientation of image grid. 2 Lindeberg 1986; Boy=-=er and Sarkar 1991; Petrou and Kittler 1991-=-; Wilson and Bhalerao 1992). 3 Another subject, which has been given large attention during recent years, is the replacement of the linear smoothing operation by a non-linear smoothing step, with the ... |

48 |
Object Shape before Boundary Shape: Scale-space Medial Axes.
- Pizer, Burbeck, et al.
- 1992
(Show Context)
Citation Context ...rowley and Parker 1984), who considered directional maxima in bandpass filtered images. During more recent years, the ridge detection problem has been intensively studied by Pizer and his co-workers (=-=Pizer et al. 1994). (Gauch -=-and Pizer 1993) define ridges from topographical watersheds computed in a scale-space representation of the image data. (Morse et al. 1994) compute "core" descriptors in a multi-scale fashio... |

39 | On optimal infinite impulse response edge detection filters”, - Sarkar - 1991 |

38 | Discrete derivative approximations with scale-space properties: A basis for low-level feature extraction.
- Lindeberg
- 1993
(Show Context)
Citation Context ...nd makes theoretical analysis possible, and (ii) it can be easily reformulated in a discrete setting and be implemented in terms of conceptually simple and generalpurpose visual front-end operations (=-=Lindeberg 1993-=-b). 6 After expanding the expressions for Lvv and Lvvv into Cartesian derivatives using (7), and selecting the numerators from the resulting rational expressions. Edge detection and ridge detection wi... |

37 | Geometry-Driven Diffusion in Computer Vision. - Romeny, Eds - 1994 |

35 | Discrete Scale-Space Theory and the Scale-Space Primal Sketch - Lindeberg - 1991 |

33 | The marching lines algorithm: new results and proofs.
- Thirion, Gourdon
- 1993
(Show Context)
Citation Context ...on approximation of the intersection of these surfaces. In this implementation, we traverse all voxels in a way closely related to the marching cubes (Lorensen and Cline 1987) and the marching lines (=-=Thirion and Gourdon 1993-=-) algorithms. For each voxel, a test is made if there the intersection of iso-surfaces passes through that voxel. Then, on top of this construction, a tracking algorithm operates and links line segmen... |

31 |
Multiscale medial analysis of medical images.
- Morse, Pizer, et al.
- 1993
(Show Context)
Citation Context ...en intensively studied by Pizer and his co-workers (Pizer et al. 1994). (Gauch and Pizer 1993) define ridges from topographical watersheds computed in a scale-space representation of the image data. (=-=Morse et al. 1994) compute "core-=-" descriptors in a multi-scale fashion by propagating a measure of edge strength from each edge point and then detecting peaks in the measure of "medialness" so obtained. A more extensi... |

30 | Toward a symbolic representation of intensity changes in images. - Korn - 1988 |

28 | Two-plus-one-dimensional differential geometry - Koenderink, Doorn - 1994 |

26 |
Scale and the di®erential structure of images
- Florack, Romeny, et al.
- 1992
(Show Context)
Citation Context ...rators to use. A systematic approach that has been developed for dealing with this problem is provided scale-space theory (Witkin 1983; Koenderink 1984; Yuille and Poggio 1986; Lindeberg 1990, 1994c; =-=Florack et al. 1992-=-). It focuses on the basic fact that image structures, like objects in the world, exist as meaningful entities over certain ranges of scale, and that one, in general, cannot expect to know in advance ... |

25 |
Modelling and identification of characteristic intensity variations,
- Rohr
- 1992
(Show Context)
Citation Context ...(Mallat and Zhong 1992), who characterize edges from the Lipschitz exponents of wavelet descriptors, (Lu and Jain 1989) who reason about the behaviour of Laplacian zero-crossings in scale-space, and (=-=Rohr 1992-=-) who fit parametric junction and edge models to the image data to estimate the degree of di#useness. The notion of scale-space edge proposed here unifies the ideas of such di#useness estimation schem... |

16 |
On scale selection for dierential operators
- Lindeberg
- 1993
(Show Context)
Citation Context ...calization step in (Lindeberg 1994a). 38 Lindeberg with explicit mechanisms for scale selection. 9 Conclusion: Principles for scale selection To conclude, this work combined with the earlier work in (=-=Lindeberg 1993-=-c, 1994a) shows that detection of local maxima over scales of normalized di#erential entities provides a consistent framework for generating hypothesis about local appropriate scales for detecting ima... |

16 | Ridge points in euclidean distance maps - Arcelli, Baja - 1992 |

15 | Sanniti di Baja, Ridge points in Euclidean distance maps - Arcelli, G - 1992 |

15 | A scale selection principle for estimating image deformations - Lindeberg - 1998 |

12 |
Visual perception by a computer
- PINGLE
- 1969
(Show Context)
Citation Context ...s at which the gradient magnitude is high. Derivative approximations were computed either from the pixels directly, using operators such as Robert's cross operator (Roberts 1965), the Sobel operator (=-=Pingle 1969-=-) and the Prewitt operator (Prewitt 1970), or from local least-squares fitting (Haralick 1984). An important step was then taken by the introduction of multi-scale techniques. (Torre and Poggio 1980) ... |

12 | Extraction of the zero-crossings of the curvature derivative in volumic 3D medical images : a multi-scale approach - Monga, Lengagne, et al. - 1994 |

12 | Kernel Designs for Efficient Multiresolution Edge Detection and Orientation Estimation - Wilson, Bhalerao - 1992 |

9 |
A representation of shape based on peaks and ridges in the dierence of low-pass transform
- Crowley, Parker
- 1984
(Show Context)
Citation Context ...tion were proposed by (Haralick 1983), who defined bright (dark) ridges as points for which the main principal curvature assumes a maximum (minimum) in the main principal curvature direction, and by (=-=Crowley and Parker 1984-=-), who considered directional maxima in bandpass filtered images. During more recent years, the ridge detection problem has been intensively studied by Pizer and his co-workers (Pizer et al. 1994). (G... |

7 | Two-plus-one-dimensional dierential geometry - Koenderink, Doorn - 1994 |

6 | Scale and segmentation of images using maximum gradient paths - Griffin, Colchester, et al. - 1992 |

5 |
Reasoning about edges in scale-space,
- Lu, Jain
- 1992
(Show Context)
Citation Context ...nature and then to fit a pre-defined model to the data. Related techniques have been presented by (Mallat and Zhong 1992), who characterize edges from the Lipschitz exponents of wavelet descriptors, (=-=Lu and Jain 1989-=-) who reason about the behaviour of Laplacian zero-crossings in scale-space, and (Rohr 1992) who fit parametric junction and edge models to the image data to estimate the degree of di#useness. The not... |

4 | Direct estimation of a#ne deformations of brightness patterns using visual front-end operators with automatic scale selection - Lindeberg - 1995 |

4 | The Structure of Images", Biological Cybernetics 50:363-370 - Koenderink, Doom - 1984 |

4 | Direct estimation of affine deformations of brightness patterns using visual front-end operators with automatic scale selection - Lindeberg - 1995 |

3 |
Shape description using weighted symmetry axis features. Pattern Recognition
- Blum, Nagel
- 1978
(Show Context)
Citation Context ...ry and discussion is given in section 7.1. Edge detection and ridge detection with automatic scale selection 23 For binary data, the related notion of "skeletons" can be derived from the med=-=ial axis (Blum and Nagel 1978-=-) and be computed by (grass-fire-like) distance transforms (Arcelli and Baja 1992). It is, however, well-known that features extracted in this way can be highly sensitive to small perturbations of the... |

2 | of Numerical Analysis and Computing - dissertation, Dept - 1991 |

1 |
Kernel design for e#cient multiresolution edge detection and orientation estimation
- Wilson, Bhalerao
- 1992
(Show Context)
Citation Context ...lse" from "true" edges. 2 In two dimensions, however, such recursive filters may be strongly biased to the orientation of image grid. 2 Lindeberg 1986; Boyer and Sarkar 1991; Petrou and=-= Kittler 1991; Wilson and Bhalerao 1992-=-). 3 Another subject, which has been given large attention during recent years, is the replacement of the linear smoothing operation by a non-linear smoothing step, with the goal of avoiding smoothing... |

1 |
Direct estimation of image deformations using visual front-end operators with automatic scale selection
- Lindeberg
- 1995
(Show Context)
Citation Context ..., corners, edges and ridges. Concerning the problem of computing local image deformations, such as optic flow and stereo matching, a related methodology for automatic scale selection is presented in (=-=Lindeberg 1995-=-). There, hypotheses about appropriate scales are generated from the scales at which normalized error measures assume local minima over scales. These suggested principles may be far more general than ... |

1 |
Scale-space filtering. 8th IJCAI, 1019--1022
- Witkin
- 1983
(Show Context)
Citation Context ...levels to the local image structure. 2 Principle for scale selection The scale-space representation L of a given signal f is obtained by convolving f by Gaussian kernels g of various widths t = oe 2 (=-=Witkin 1983-=-, Koenderink 1984, Florack et al. 1992, Lindeberg 1994). From this representation, a scale-space derivative is defined by L x ff y fi (\Delta; t) = @ x ff y fi (g(\Delta; t)sf) = g x ff y fi (\Delta; ... |

1 | Scale-space ltering. 8th IJCAI, 1019{1022 - Witkin - 1983 |