## Feature detection with automatic scale selection (1998)

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Venue: | International Journal of Computer Vision |

Citations: | 486 - 25 self |

### BibTeX

@ARTICLE{Lindeberg98featuredetection,

author = {Tony Lindeberg},

title = {Feature detection with automatic scale selection},

journal = {International Journal of Computer Vision},

year = {1998},

volume = {30},

pages = {79--116}

}

### Years of Citing Articles

### OpenURL

### Abstract

The fact that objects in the world appear in different ways depending on the scale of observation has important implications if one aims at describing them. It shows that the notion of scale is of utmost importance when processing unknown measurement data by automatic methods. In their seminal works, Witkin (1983) and Koenderink (1984) proposed to approach this problem by representing image structures at different scales in a so-called scale-space representation. Traditional scale-space theory building on this work, however, does not address the problem of how to select local appropriate scales for further analysis. This article proposes a systematic methodology for dealing with this problem. A framework is proposed for generating hypotheses about interesting scale levels in image data, based on a general principle stating that local extrema over scales of different combinations of γ-normalized derivatives are likely candidates to correspond to interesting structures. Specifically, it is shown how this idea can be used as a major mechanism in algorithms for automatic scale selection, which

### Citations

660 |
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Citation Context ...ave lead to the construction of multi-scale representations of image data, obtained by embedding any given signal into a one-parameter family of derived signals (Burt 1981; Crowley 1981; Witkin 1983; =-=Koenderink 1984-=-; Yuille and Poggio 1986; Florack et al. 1992; Lindeberg 1994d; Haar Romeny 1994). This family should be parameterized by a scale parameter and be generated in such a way that fine-scale structures ar... |

605 | Relations between the statistics of natural images and the response properties of cortical cells
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Citation Context ...m(1-#) . (90) In the special case when D = 2 and # = 1, this corresponds to power spectra of the form |#| -2 . It is well-known that natural images often show a qualitative behaviour similar to this (=-=Field 1987-=-). This is in fact a direct consequence of scale invariance; the power spectrum variation S(#) # |#| -D , (91) where D is the dimension of the signal, can be easily derived 9 directly from the 9 To de... |

539 |
Scale-Space Filtering
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Citation Context ...se insights have lead to the construction of multi-scale representations of image data, obtained by embedding any given signal into a one-parameter family of derived signals (Burt 1981; Crowley 1981; =-=Witkin 1983-=-; Koenderink 1984; Yuille and Poggio 1986; Florack et al. 1992; Lindeberg 1994d; Haar Romeny 1994). This family should be parameterized by a scale parameter and be generated in such a way that fine-sc... |

492 |
Characterization of signals from multiscale edges
- Mallat, Zhong
- 1992
(Show Context)
Citation Context ...mount of energy for all frequencies. 9.3 Relations to previous work Such L 1 -normalized kernels of first order have been used, for example, in edge detection and edge classification by (Korn 1988), (=-=Mallat and Zhong 1992-=-), and (Zhang and Bergholm 1993), and in pyramids by (Crowley and Parker 1984). More generally, evolution properties across scales of wavelet transforms have been used by (Mallat and Hwang 1992) for c... |

386 | Singularity detection and processing with wavelets
- Mallat, Hwang
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(Show Context)
Citation Context ...m ) = (#m) #m/2 e #m/2 # (1-#)m 0 . (13) 1 An analysis of scale-space like responses to sine waves corresponding to the case when # = 1 in this section has also been performed in wavelet analysis by (=-=Mallat and Hwang 1992-=-); see section 9.3. Feature detection with automatic scale selection 5 In the case when # = 1, this maximum value is independent of the frequency of the signal (see figure 1), and the situation is hig... |

248 | Edge detection and ridge detection with automatic scale selection
- Lindeberg
- 1998
(Show Context)
Citation Context ...feature maps. Section 9 describes di#erent ways of interpreting the normalized derivative concept. Finally, section 10 summarizes the main results and ideas of the approach. In a complementary paper (=-=Lindeberg 1996-=-a) it is developed in detail how this approach applies to edge detection and ridge detection. Earlier presentations of di#erent parts of this material have appeared elsewhere (Lindeberg 1993b, 1994a, ... |

208 |
E.: A fast operator for detection and precise location of distinct points, corners and centres of circular features
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Citation Context ...ate. Given an approximate estimate x 0 of the location and the size s of a corner (computed according to section 6), an improved estimate of the corner position can be computed as follows: Following (=-=Forstner and Gulch 1987-=-), consider at every point x # # R 2 in a neighbourhood of a junction candidate x 0 , the line l x # perpendicular to the gradient vector (#L)(x # ) = (L x 1 , L x 2 ) T (x # ) at that point: D x # (x... |

149 | Detecting salient blob-like image structures and their scales with a scale-space primal sketch
- Lindeberg
- 1993
(Show Context)
Citation Context ...ry paper (Lindeberg 1996a) it is developed in detail how this approach applies to edge detection and ridge detection. Earlier presentations of di#erent parts of this material have appeared elsewhere (=-=Lindeberg 1993-=-b, 1994a, 1994d, 1996b) as well as applications of the general ideas to Feature detection with automatic scale selection 3 various problem domains (Lindeberg and Garding 1993, 1997; Garding and Lindeb... |

147 | Scaling theorems for zero crossings
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Citation Context ...onstruction of multi-scale representations of image data, obtained by embedding any given signal into a one-parameter family of derived signals (Burt 1981; Crowley 1981; Witkin 1983; Koenderink 1984; =-=Yuille and Poggio 1986-=-; Florack et al. 1992; Lindeberg 1994d; Haar Romeny 1994). This family should be parameterized by a scale parameter and be generated in such a way that fine-scale structures are successively suppresse... |

137 |
Uniqueness of the Gaussian kernel for scale-space filtering
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- 1986
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Citation Context ...; t) = g(; t) # f(), (2) where g : R D R+ # R is given by g(x; t) = 1 (2#t) N/2 e -(x 2 1 +...+x 2 D )/(2t) , (3) and x = (x 1 , ..., xD ) T . There are several mathematical results (Koenderink 1984; =-=Babaud et al. 1986-=-; Yuille and Poggio 1986; Lindeberg 1990, 1994d, 1994b; Koenderink and van Doorn 1990, 1992; Florack et al. 1992; Florack 1993; Florack et al. 1994; Pauwels et al. 1995) stating that within the class ... |

124 |
Fast filter transforms for image processing
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- 1981
(Show Context)
Citation Context ...and image processing, these insights have lead to the construction of multi-scale representations of image data, obtained by embedding any given signal into a one-parameter family of derived signals (=-=Burt 1981-=-; Crowley 1981; Witkin 1983; Koenderink 1984; Yuille and Poggio 1986; Florack et al. 1992; Lindeberg 1994d; Haar Romeny 1994). This family should be parameterized by a scale parameter and be generated... |

123 |
Gray-level corner detection
- Kitchen, Rosenfeld
- 1982
(Show Context)
Citation Context ...Selection of detection scales from normalized scale-space maxima A commonly used entity for junction detection is the curvature of level curves in intensity data multiplied by the gradient magnitude (=-=Kitchen and Rosenfeld 1982-=-; Dreschler and Nagel 1982; Koenderink and Richards 1988; Noble 1988; Deriche and Giraudon 1990; Blom 1992; Florack et al. 1992; Lindeberg 1994d). A special choice is to multiply the level curve curva... |

94 | Scale-space for discrete signals
- Lindeberg
- 1990
(Show Context)
Citation Context ...R is given by g(x; t) = 1 (2#t) N/2 e -(x 2 1 +...+x 2 D )/(2t) , (3) and x = (x 1 , ..., xD ) T . There are several mathematical results (Koenderink 1984; Babaud et al. 1986; Yuille and Poggio 1986; =-=Lindeberg 1990-=-, 1994d, 1994b; Koenderink and van Doorn 1990, 1992; Florack et al. 1992; Florack 1993; Florack et al. 1994; Pauwels et al. 1995) stating that within the class of linear transformations the Gaussian k... |

91 |
A representation for shape based on peaks and ridges in the difference of low pass transform
- Crowley, Parker
(Show Context)
Citation Context ...L1-normalized kernels of first order have been used, for example, in edge detection and edge classification by (Korn 1988), (Mallat and Zhong 1992), and (Zhang and Bergholm 1993), and in pyramids by (=-=Crowley and Parker 1984-=-). More generally, evolution properties across scales of wavelet transforms have been used by (Mallat and Hwang 1992) for characterizing local Lipshitz exponents of singularities. (Mallat and Hwang 19... |

81 |
Scale-space Theory in Computer Vision. The Kluwer
- Lindeberg
- 1994
(Show Context)
Citation Context ...tes a set of junction candidates. 5 Besides the general descriptions given in previous sections, further details concerning algorithms and discrete implementation can be found in appendix A.4 and in (=-=Lindeberg 1994-=-c). 28 Lindeberg localized junctions (detection scale) localized junctions (localization scale) Figure 15: Improved localization estimates for the junction candidates in figure 8. Each junction has be... |

77 |
Volumetric model and 3d trajectory of a moving car derived from monocular tv frame sequences of a street scene
- Dreschler, Nagel
- 1982
(Show Context)
Citation Context ...s from normalized scale-space maxima A commonly used entity for junction detection is the curvature of level curves in intensity data multiplied by the gradient magnitude (Kitchen and Rosenfeld 1982; =-=Dreschler and Nagel 1982-=-; Koenderink and Richards 1988; Noble 1988; Deriche and Giraudon 1990; Blom 1992; Florack et al. 1992; Lindeberg 1994d). A special choice is to multiply the level curve curvature by the gradient magni... |

68 | Shape-adapted smoothing in estimation of 3-D depth cues from affine distortions of local 2-D brightness structure - Lindeberg, G˚arding |

54 | Direct computation of shape cues using scale-adapted spatial derivative operators,”Int’l
- Garding, Lindeberg
(Show Context)
Citation Context ...re (Lindeberg 1993b, 1994a, 1994d, 1996b) as well as applications of the general ideas to Feature detection with automatic scale selection 3 various problem domains (Lindeberg and Garding 1993, 1997; =-=Garding and Lindeberg 1996-=-; Lindeberg and Li 1995, 1997; Bretzner and Lindeberg 1998, 1997; Almansa and Lindeberg 1996; Wiltschi et al. 1997; Lindeberg 1997). The subject of this paper is to present a coherent description of t... |

52 | Receptive Field Families - Koenderink, Doom - 1990 |

48 |
The Gaussian derivative theory of spatial vision: analysis of cortical cell receptive field line-weighting profiles. Warren, Mich.: General Motors Research Laboratories
- Young
- 1985
(Show Context)
Citation Context ...from a finer to a coarser scale. Interestingly, the results from these theoretical considerations are in qualitative agreement with the results of biological evolution. Neurophysiological studies by (=-=Young 1985-=-, 1987) have shown that there are receptive fields in the mammalian retina and visual cortex, whose measured response profiles can be well modelled by Gaussian derivatives up to order four. In these r... |

48 | Scale selection for differential operators
- Lindeberg
- 1994
(Show Context)
Citation Context ...y paper (Lindeberg 1996a) it is developed in detail how this approach applies to edge detection and ridge detection. Earlier presentations of different parts of this material have appeared elsewhere (=-=Lindeberg 1993-=-b, 1994a, 1994d, 1996b) as well as applications of the general ideas tosFeature detection with automatic scale selection 3 various problem domains (Lindeberg and G˚arding 1993, 1997; G˚arding and Lind... |

38 | Fingerprint Enhancement Shaped Adaptation of Scale-Space Operators with Automatic Scale Selection - ALMANSA, LINDEBERG - 2000 |

38 | Shape from texture from a multi-scale perspective
- Lindeberg, Garding
- 1993
(Show Context)
Citation Context ...his material have appeared elsewhere (Lindeberg 1993b, 1994a, 1994d, 1996b) as well as applications of the general ideas to Feature detection with automatic scale selection 3 various problem domains (=-=Lindeberg and Garding 1993-=-, 1997; Garding and Lindeberg 1996; Lindeberg and Li 1995, 1997; Bretzner and Lindeberg 1998, 1997; Almansa and Lindeberg 1996; Wiltschi et al. 1997; Lindeberg 1997). The subject of this paper is to p... |

36 |
Nonlinear scale-space
- Florack, Salden, et al.
- 1995
(Show Context)
Citation Context ...re are several mathematical results (Koenderink 1984; Babaud et al. 1986; Yuille and Poggio 1986; Lindeberg 1990, 1994d, 1994b; Koenderink and van Doorn 1990, 1992; Florack et al. 1992; Florack 1993; =-=Florack et al. 1994-=-; Pauwels et al. 1995) stating that within the class of linear transformations the Gaussian kernel is the unique kernel for generating a scale-space. The conditions that specify the uniqueness are ess... |

28 | An extended class of scaleinvariant and recursive scale space filters - Pauwels, Gool, et al. - 1995 |

27 |
Two-dimensional curvature operators
- Koenderink, Richards
- 1988
(Show Context)
Citation Context ...ace maxima A commonly used entity for junction detection is the curvature of level curves in intensity data multiplied by the gradient magnitude (Kitchen and Rosenfeld 1982; Dreschler and Nagel 1982; =-=Koenderink and Richards 1988-=-; Noble 1988; Deriche and Giraudon 1990; Blom 1992; Florack et al. 1992; Lindeberg 1994d). A special choice is to multiply the level curve curvature by the gradient magnitude raised to the power of th... |

27 |
Toward a symbolic representation of intensity changes in images
- Korn
- 1988
(Show Context)
Citation Context ...in the same amount of energy for all frequencies. 9.3 Relations to previous work Such L 1 -normalized kernels of first order have been used, for example, in edge detection and edge classification by (=-=Korn 1988-=-), (Mallat and Zhong 1992), and (Zhang and Bergholm 1993), and in pyramids by (Crowley and Parker 1984). More generally, evolution properties across scales of wavelet transforms have been used by (Mal... |

23 | A multiscale region detector
- Blostein, Ahuja
- 1989
(Show Context)
Citation Context ...e reason why these particular di#erential expressions have been selected here is because they constitute di#erential entities useful for blob detection; see e.g. (Marr 1982; Voorhees and Poggio 1987; =-=Blostein and Ahuja 1989-=-). Before we turn to the problem of expressing an integrated blob detector with automatic scale selection, however, let us describe a further extension of the general scale selection idea. 4.4 Simulta... |

22 |
Representing signals by their toppoints in scale-space
- Johansen, Skelboe, et al.
- 1986
(Show Context)
Citation Context ... in (Lindeberg 1991, 1993a) based on local maxima over scales of blob responses computed along extremum paths in scale-space. There is also a connection to the "top point" representation pro=-=posed by (Johansen et al. 1986-=-) in the sense that the points in the scale-space at which bifurcations occur serve as to delimit extremum paths with di#erent topology. A main di#erence between the scale selection mechanism suggeste... |

19 | Active detection and classification of junctions by foveation with a head-eye system guided by the scale-space primal sketch - Brunnstrom, Lindeberg, et al. - 1992 |

19 |
A representation for visual information
- Crowley
- 1981
(Show Context)
Citation Context ...rocessing, these insights have lead to the construction of multi-scale representations of image data, obtained by embedding any given signal into a one-parameter family of derived signals (Burt 1981; =-=Crowley 1981-=-; Witkin 1983; Koenderink 1984; Yuille and Poggio 1986; Florack et al. 1992; Lindeberg 1994d; Haar Romeny 1994). This family should be parameterized by a scale parameter and be generated in such a way... |

18 | Junction detection with automatic selection of detection scales and localization scales
- Lindeberg
- 1994
(Show Context)
Citation Context ... image data, obtained by embedding any given signal into a one-parameter family of derived signals (Burt 1981; Crowley 1981; Witkin 1983; Koenderink 1984; Yuille and Poggio 1986; Florack et al. 1992; =-=Lindeberg 1994-=-d; Haar Romeny 1994). This family should be parameterized by a scale parameter and be generated in such a way that fine-scale structures are successively suppressed when the scale parameter is increas... |

13 |
On scale selection for di erential operators, in
- Lindeberg
- 1993
(Show Context)
Citation Context ...ry paper (Lindeberg 1996a) it is developed in detail how this approach applies to edge detection and ridge detection. Earlier presentations of di#erent parts of this material have appeared elsewhere (=-=Lindeberg 1993-=-b, 1994a, 1994d, 1996b) as well as applications of the general ideas to Feature detection with automatic scale selection 3 various problem domains (Lindeberg and Garding 1993, 1997; Garding and Lindeb... |

11 | Segmentation and classification of edges using minimum description length approximation and complementary junction cues, Computer Vision and Image Understanding - Lindeberg, Li |

11 | A scale selection principle for estimating image deformations
- Lindeberg
- 1996
(Show Context)
Citation Context ...he problem of edge detection, and that further processing steps are needed to give a complete algorithm. A complementary scale selection method applicable in the edge detection stage is presented in (=-=Lindeberg 1996-=-a). 8 Dense frequency estimation So far, we have seen how the scale selection methodology can be applied to the detection of sparse feature points. In certain situations, however, one is also interest... |

10 | On the Axiomatic Foundations of Linear Scale-Space: Combining Semi-Group Structure with Causality vs. Scale Invariance
- Lindeberg
- 1994
(Show Context)
Citation Context ...tes a set of junction candidates. 5 Besides the general descriptions given in previous sections, further details concerning algorithms and discrete implementation can be found in appendix A.4 and in (=-=Lindeberg 1994-=-c). 28 Lindeberg localized junctions (detection scale) localized junctions (localization scale) Figure 15: Improved localization estimates for the junction candidates in figure 8. Each junction has be... |

8 |
A representation for shape based on peaks and ridges in the di erence of low-pass transform
- Crowley, Parker
- 1984
(Show Context)
Citation Context ...1 -normalized kernels of first order have been used, for example, in edge detection and edge classification by (Korn 1988), (Mallat and Zhong 1992), and (Zhang and Bergholm 1993), and in pyramids by (=-=Crowley and Parker 1984-=-). More generally, evolution properties across scales of wavelet transforms have been used by (Mallat and Hwang 1992) for characterizing local Lipshitz exponents of singularities. (Mallat and Hwang 19... |

4 |
Direct estimation of a#ne deformations of brightness patterns using visual front-end operators with automatic scale selection
- Lindeberg
- 1995
(Show Context)
Citation Context ...that undergo large size changes. Moreover, the scale information associated with each junction can be used as an important matching cue in its own right and be included in the matching criterion. In (=-=Lindeberg 1995-=-a, 1996d) a scale selection principle for stereo matching and flow estimation is presented, which also involves the extension of a fixed scale least squares estimation problem to optimization over mul... |

3 |
Scale Selection for Di#erential Operators". Technical Report ISRN KTH/NA/P--94/03--SE, Dept. of Numerical Analysis and Computing Science
- Lindeberg
- 1994
(Show Context)
Citation Context ... image data, obtained by embedding any given signal into a one-parameter family of derived signals (Burt 1981; Crowley 1981; Witkin 1983; Koenderink 1984; Yuille and Poggio 1986; Florack et al. 1992; =-=Lindeberg 1994-=-d; Haar Romeny 1994). This family should be parameterized by a scale parameter and be generated in such a way that fine-scale structures are successively suppressed when the scale parameter is increas... |

3 |
Direct estimation of affine deformations of brightness patterns using visual front-end operators with automatic scale selection
- Lindeberg
- 1995
(Show Context)
Citation Context ...that undergo large size changes. Moreover, the scale information associated with each junction can be used as an important matching cue in its own right and be included in the matching criterion. In (=-=Lindeberg 1995-=-a, 1996d) a scale selection principle for stereo matching and flow estimation is presented, which also involves the extension of a fixed scale least squares estimation problem to optimization over mul... |

2 |
Enhancement of fingerprint images by shape-adapted scale-space operators
- Almansa, Lindeberg
(Show Context)
Citation Context ...ature detection with automatic scale selection 3 various problem domains (Lindeberg and Garding 1993, 1997; Garding and Lindeberg 1996; Lindeberg and Li 1995, 1997; Bretzner and Lindeberg 1998, 1997; =-=Almansa and Lindeberg 1996-=-; Wiltschi et al. 1997; Lindeberg 1997). The subject of this paper is to present a coherent description of the proposed scale selection methodology in journal form, including the developments and refi... |

2 | Classification of carbide distributions using scale selection and directional information
- Wiltschi, Lindeberg
- 1997
(Show Context)
Citation Context ...ic scale selection 3 various problem domains (Lindeberg and Garding 1993, 1997; Garding and Lindeberg 1996; Lindeberg and Li 1995, 1997; Bretzner and Lindeberg 1998, 1997; Almansa and Lindeberg 1996; =-=Wiltschi et al. 1997-=-; Lindeberg 1997). The subject of this paper is to present a coherent description of the proposed scale selection methodology in journal form, including the developments and refinements that have been... |

1 | Feature tracking with automatic selection of spatial scales - Scale-Space'97 - 1997 |

1 | Feature detection with automatic scale selection 49 - Utrecht, Netherlands - 1993 |

1 |
The Aspect Feature Graph in Recognition by Parts". draft manuscript
- Lindeberg, Olofsson
- 1995
(Show Context)
Citation Context ...in a pre-processing stage for classifying edges into straight and curved. More generally, such relations between edges and junctions are also useful for other problems relating to object recognition (=-=Lindeberg and Olofsson 1995-=-). In (Bretzner and Lindeberg 1996) it is demonstrated how these support regions can be used for simplifying matching of junctions over time in tracking algorithms. Specifically, it is shown that the ... |

1 | of Numerical Analysis and Computing Science - dissertation, Dept - 1991 |

1 |
On scale selection in subsampled (hybrid) multi-scale representations
- Lindeberg
- 1995
(Show Context)
Citation Context ...that undergo large size changes. Moreover, the scale information associated with each junction can be used as an important matching cue in its own right and be included in the matching criterion. In (=-=Lindeberg 1995-=-a, 1996d) a scale selection principle for stereo matching and flow estimation is presented, which also involves the extension of a fixed scale least squares estimation problem to optimization over mul... |

1 | Feature detection with automatic scale selection 51 - Freeman - 1982 |

1 |
Feature detection with automatic scale selection 49
- Florack, Romeny, et al.
- 1992
(Show Context)
Citation Context ...le representations of image data, obtained by embedding any given signal into a one-parameter family of derived signals (Burt 1981; Crowley 1981; Witkin 1983; Koenderink 1984; Yuille and Poggio 1986; =-=Florack et al. 1992-=-; Lindeberg 1994d; Haar Romeny 1994). This family should be parameterized by a scale parameter and be generated in such a way that fine-scale structures are successively suppressed when the scale para... |

1 |
The Aspect Feature Graph in Recognition by Parts”. draft manuscript
- Lindeberg, Olofsson
- 1995
(Show Context)
Citation Context ...in a pre-processing stage for classifying edges into straight and curved. More generally, such relations between edges and junctions are also useful for other problems relating to object recognition (=-=Lindeberg and Olofsson 1995-=-). In (Bretzner and Lindeberg 1996) it is demonstrated how these support regions can be used for simplifying matching of junctions over time in tracking algorithms. Specifically, it is shown that the ... |