## A Survey of Shape Analysis Techniques (1998)

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Venue: | Pattern Recognition |

Citations: | 218 - 2 self |

### BibTeX

@ARTICLE{Loncaric98asurvey,

author = {Sven Loncaric},

title = {A Survey of Shape Analysis Techniques},

journal = {Pattern Recognition},

year = {1998},

volume = {31},

pages = {983--1001}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.

### Citations

8181 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context .... Multiple SEs are obtained by rotating single or multiple original structuring elements. A method for near-optimal shape matching using MST was developed in [176]. It is based on a genetic algorithm =-=[177, 178, 179]-=- for selection of a near-optimal structuring element for MST shape description. The selected SE provides nearly the best discrimination of shapes from a given class. 27s6 Global Space Domain Technique... |

4145 |
Pattern Classification and Scene Analysis
- Duda, Hart
- 1973
(Show Context)
Citation Context ...scriptor vectors using a metric. The problem of the shape analysis has been pursued by many authors thus resulting in a great amount of research. A number of review papers [1, 2, 3], as well as books =-=[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]-=- have been written on the subject of shape analysis. 1.1 Classifications Shape analysis methods can be classified according to many different criteria. Pavlidis [1] has proposed the following classifi... |

3665 |
Fuzzy sets
- Zadeh
- 1965
(Show Context)
Citation Context ...inearity [41]. This method was based on heuristics based on human concepts of collinearity. Experiments veri ed the e ectiveness of the approach. Vanderheydt et al. [212] used the fuzzy subset theory =-=[213, 214]-=- to direct decomposition based on convex and concave boundary points and 32spolygonal approximation of the boundary. The method was applied to the problem of chromosome shape analysis. Sanniti and Thi... |

3135 |
Genetic Programming: On the Programming of Computers by Means of Natural Selection
- Koza
- 1992
(Show Context)
Citation Context .... Multiple SEs are obtained by rotating single or multiple original structuring elements. A method for near-optimal shape matching using MST was developed in [176]. It is based on a genetic algorithm =-=[177, 178, 179]-=- for selection of a near-optimal structuring element for MST shape description. The selected SE provides nearly the best discrimination of shapes from a given class. 27s6 Global Space Domain Technique... |

1934 |
The Fractal Geometry of Nature
- Mandelbrot
- 1983
(Show Context)
Citation Context ...evel of control all levels bellow any given level are also included in information processing. Pentland [99, 100] investigated methods for representation of natural forms by means of fractal geometry =-=[101, 102, 103]-=-. He argued that fractal functions are appropriate for natural shape representation because many physical processes produce fractal surface shapes. This is due to the fact that natural forms repeat wh... |

1483 |
Robot Vision
- Horn
- 1986
(Show Context)
Citation Context ...scriptor vectors using a metric. The problem of the shape analysis has been pursued by many authors thus resulting in a great amount of research. A number of review papers [1, 2, 3], as well as books =-=[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]-=- have been written on the subject of shape analysis. 1.1 Classi cations Shape analysis methods can be classi ed according to many di erent criteria. Pavlidis [1] has proposed the following classi cati... |

1293 | Handbook of Genetic Algorithm
- Davis
- 1991
(Show Context)
Citation Context .... Multiple SEs are obtained by rotating single or multiple original structuring elements. A method for near-optimal shape matching using MST was developed in [176]. It is based on a genetic algorithm =-=[177, 178, 179]-=- for selection of a near-optimal structuring element for MST shape description. The selected SE provides nearly the best discrimination of shapes from a given class. 27s6 Global Space Domain Technique... |

1259 |
A Practical Guide to Splines
- Boor
- 1978
(Show Context)
Citation Context ...imation of curves. Ikebe and Miyamoto [139] wrote an overview of spline applications for shape design, representation, and restoration. Mathematical treatment of splines is presented in several books =-=[140, 141, 142]-=-, while the computer graphics 19sperspective is presented in [143, 144, 145, 146]. Splines posses the bene cial property of minimizing curvature. In other words, they approximate a given function with... |

1218 |
Image Analysis and Mathematical Morphology
- Serra
- 1982
(Show Context)
Citation Context ...The authors demonstrated that the shape vector scheme can be used for shape matching. 5.3 Morphological Methods Mathematical morphology has evolved as a useful tool for various image processing tasks =-=[161, 162, 163, 164, 165]-=-. It is suitable for shape-related processing since morphological operations are directly related to the object shape. It is rst necessary to introduce some basic de nitions related to mathematical mo... |

1112 |
The organization of behavior
- Hebb
- 1949
(Show Context)
Citation Context ...operties in di erent directions. Another approach to the theory of visual form is found in Hebb's work. Hebb presented a neuropsychological theory of behavior in his book The Organization of Behavior =-=[59]-=-. In his theory, Hebb emphasized the role of neural structures in the mechanism of visual perception. His work in uenced a number of researchers in the eld of arti cial neural networks. As opposed to ... |

949 | Theory of edge detection
- Marr, Hildreth
- 1979
(Show Context)
Citation Context ...ave no corresponding stimulus in the real world). A tutorial on visual cognition with an emphasis on shape recognition was written by Pinker [61]. 2.2 Modern Theories of Visual Perception Marr et al. =-=[62, 63, 43, 64, 65, 66]-=- made signi cant contributions to the study of the human visual perception system. In Marr's paradigm [67], the focus of research is shifted from applications to topics corresponding to modules of the... |

886 |
Visual pattern recognition by moment invariants
- Hu
- 1962
(Show Context)
Citation Context ...7, 28, 29]. Examples of global methods include the medial axis (also called symmetric axis) transform (MAT) proposed by Blum and described in [30, 31, 32, 17, 33, 34, 20, 22], moment based approaches =-=[35, 36, 37, 38]-=-, and methods of shape decomposition into other primitive shapes [39, 40, 41, 42]. Another classi cation of shape analysis algorithms can be made on the basis of whether the result of the analysis is ... |

870 |
Computer Vision
- Ballard, Brown
- 1982
(Show Context)
Citation Context ...scriptor vectors using a metric. The problem of the shape analysis has been pursued by many authors thus resulting in a great amount of research. A number of review papers [1, 2, 3], as well as books =-=[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]-=- have been written on the subject of shape analysis. 1.1 Classi cations Shape analysis methods can be classi ed according to many di erent criteria. Pavlidis [1] has proposed the following classi cati... |

762 |
Fractals everywhere
- Barnsley
- 1988
(Show Context)
Citation Context ...evel of control all levels bellow any given level are also included in information processing. Pentland [99, 100] investigated methods for representation of natural forms by means of fractal geometry =-=[101, 102, 103]-=-. He argued that fractal functions are appropriate for natural shape representation because many physical processes produce fractal surface shapes. This is due to the fact that natural forms repeat wh... |

702 |
An Introduction to Signal Detection and Estimation
- Poor
- 1994
(Show Context)
Citation Context ...quation rt = + mX j=1 jrt,j + p !t where !i are independent random noise sources. The parameters f ; 1;:::; m; g are unknown and need to be estimated. The maximum likelihood (ML) parameter estimation =-=[113, 114, 115]-=- was used. The ML estimated parameters i are translation, rotation, and scale invariant. Note that the rotation invariance holds only for angles that are multiples of 2 =N . Parameters and are not sca... |

697 |
The structure of images
- Koenderink
- 1984
(Show Context)
Citation Context ... crossings of the Laplacian of the two-dimensional Gaussian distribution function. In this approach, zeros of Laplacian indicate the in ection point in the edge to detect edge positions. 8sKoenderink =-=[73]-=- and Koenderink and van Doorn [74] have studied the psychological aspects of visual perception and proposed several interesting paradigms. Conventional approaches to shape are often static in the sens... |

694 |
Pattern Recognition: A Statistical Approach
- Devijver, Kittler
- 1982
(Show Context)
Citation Context ...groups the members of one pattern class closer in the new coordinate system. The third modi cation included the use of hyper-planes to divide the pattern space. The least mean squared error procedure =-=[118]-=- yields the optimal hyper-plane parameters. The experimental result showed that the normalized AR model parameters useful shape descriptors. A modi cation of the Dubois and Glanz method included stati... |

641 |
Outline of a new approach to the analysis of complex systems and decision processes
- Zadeh
- 1973
(Show Context)
Citation Context ...inearity [41]. This method was based on heuristics based on human concepts of collinearity. Experiments veri ed the e ectiveness of the approach. Vanderheydt et al. [212] used the fuzzy subset theory =-=[213, 214]-=- to direct decomposition based on convex and concave boundary points and 32spolygonal approximation of the boundary. The method was applied to the problem of chromosome shape analysis. Sanniti and Thi... |

566 |
Scale-Space Filtering
- Witkin
- 1983
(Show Context)
Citation Context ...nted a hierarchical method where the shape boundary is represented by a polygonal approximation. The split-and-merge algorithm was used to create the polygonal approximation. The scale-space approach =-=[138]-=- was used to track the position of inflection points on the boundary curve. Stable shape features are those which remain unchanged over scale. Tangents at border points are estimated using a polynomia... |

518 |
A transformation for extracting new descriptors of shape
- Blum
- 1967
(Show Context)
Citation Context ... and various Fourier transforms of the boundary [25, 26, 27, 28, 29]. Examples of global methods include the medial axis (also called symmetric axis) transform (MAT) proposed by Blum and described in =-=[30, 31, 32, 17, 33, 34, 20, 22]-=-, moment based approaches [35, 36, 37, 38], and methods of shape decomposition into other primitive shapes [39, 40, 41, 42]. Another classi cation of shape analysis algorithms can be made on the basis... |

505 |
Principles of gestalt psychology
- Koffka
- 1935
(Show Context)
Citation Context ...f selected topics. The Gestalt school of psychology [54] has played a revolutionary role with its novel approach to visual form. A detailed exposition of the subject of Gestalt theory can be found in =-=[55, 56, 57, 58]. The-=- Gestalt theory is a non-computational theory of visual form, and thus a disadvantage for practical engineering applications. However, according to Zusne "it is still the only theory to deal with... |

497 |
Representation and recognition of the spatial organization of three-dimensional shapes
- Marr, Nishihara
- 1978
(Show Context)
Citation Context ...ll do not exist for shape description methods. Several authors have proposed evaluation criteria in the form of lists of qualities that a good shape description method should have. Marr and Nishihara =-=[43]-=- proposed a set of criteria for the evaluation of shape description methods: accessibility, scope and uniqueness, and stability and sensitivity. Accessibility describes how easy (or di cult) it is to ... |

478 |
Random Sets and Integral Geometry
- Matheron
- 1975
(Show Context)
Citation Context ...The authors demonstrated that the shape vector scheme can be used for shape matching. 5.3 Morphological Methods Mathematical morphology has evolved as a useful tool for various image processing tasks =-=[161, 162, 163, 164, 165]-=-. It is suitable for shape-related processing since morphological operations are directly related to the object shape. It is rst necessary to introduce some basic de nitions related to mathematical mo... |

473 | Some informational aspects of visual perception
- Attneave
- 1954
(Show Context)
Citation Context ...di erential equation that describes the evolution of the shape through multiple resolutions. Many authors agree on the signi cance of high curvature points for visual perception. Attneave and Arnoult =-=[76, 77]-=- performed psychological experiments to investigate the signi cance of corners for perception. In the famous Attneave's cat experiment a drawing of a cat was used to locate points of high curvature wh... |

472 |
Perceptual Organization and Visual Recognition
- Lowe
- 1985
(Show Context)
Citation Context ...An exhaustive survey of human visual perception research is beyond the scope of this paper. Some introductory and more advanced books and articles dealing with visual perception and cognition include =-=[4, 46, 47,48,49,50,51,52]-=-. In this section, a brief overview of visual perception research related to shape description is presented. 2.1 Classical Theories of Visual Perception Several schools of psychology have endeavored t... |

447 |
The perception of the visual world
- Gibson
- 1950
(Show Context)
Citation Context ...s causing neurons in the group to mutually excite each other. Hebb's theory was mostly qualitative and not computational, thus presenting a disadvantage for practical engineering applications. Gibson =-=[60]-=- developed another comprehensive theory of visual perception. The rst principle of his theory is that space is not a geometric or abstract entity, but a real visual one characterized by the forms that... |

414 | Three-dimensional object recognition from single two-dimensional images
- Lowe
- 1987
(Show Context)
Citation Context ...oped for engineering purposes and not necessarily to study perception. Fractal representations produce objects which correspond much better to the human model of visual perception and cognition. Lowe =-=[106]-=- proposed a computer vision system that can recognize three-dimensional objects from unknown viewpoints and single two-dimensional images. The procedure is non-typical and uses three mechanisms of per... |

361 |
A computational theory of human stereo vision
- Marr, Poggio
- 1979
(Show Context)
Citation Context ...ave no corresponding stimulus in the real world). A tutorial on visual cognition with an emphasis on shape recognition was written by Pinker [61]. 2.2 Modern Theories of Visual Perception Marr et al. =-=[62, 63, 43, 64, 65, 66]-=- made signi cant contributions to the study of the human visual perception system. In Marr's paradigm [67], the focus of research is shifted from applications to topics corresponding to modules of the... |

345 |
An Introduction to Numerical Analysis
- Atkinson
- 1989
(Show Context)
Citation Context ...imation of curves. Ikebe and Miyamoto [139] wrote an overview of spline applications for shape design, representation, and restoration. Mathematical treatment of splines is presented in several books =-=[140, 141, 142]-=-, while the computer graphics 19sperspective is presented in [143, 144, 145, 146]. Splines posses the bene cial property of minimizing curvature. In other words, they approximate a given function with... |

345 |
Distance transformations in digital images
- Borgefors
- 1986
(Show Context)
Citation Context ...nd a group was disquali ed if less then three consecutive segments matched. The nal step was used to measure the distance between two shapes. This was done by using the Chamfer 3=4 distance transform =-=[157, 158]-=- which approximates the Euclidean distance transform very well, but is less computationally intensive. The Chamfer 3=4 distance transform was computed for the 21srst boundary; the second boundary was ... |

293 |
Differential topology
- Guillemin, Pollack
- 1974
(Show Context)
Citation Context ...c medical images). Hoffman and Richards [94, 95] argue that when the visual system decomposes objects it does so at points of high negative curvature. This agrees with the principle of transversality =-=[96]-=- found in nature. The principle of transversality contends that when two arbitrarily shaped convex objects interpenetrate each other, the meeting point is a boundary point of concave discontinuity of ... |

279 |
An Introduction to Splines for Use in Computer Graphics and Geometric Modelling
- Bartels
- 1987
(Show Context)
Citation Context ...ications for shape design, representation, and restoration. Mathematical treatment of splines is presented in several books [140, 141, 142], while the computer graphics 19sperspective is presented in =-=[143, 144, 145, 146]-=-. Splines posses the bene cial property of minimizing curvature. In other words, they approximate a given function with a curve having the minimum average curvature. This makes them perfect candidates... |

270 |
Pattern Classi cation and Scene Analysis
- Duda, Hart
- 1973
(Show Context)
Citation Context ...scriptor vectors using a metric. The problem of the shape analysis has been pursued by many authors thus resulting in a great amount of research. A number of review papers [1, 2, 3], as well as books =-=[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]-=- have been written on the subject of shape analysis. 1.1 Classi cations Shape analysis methods can be classi ed according to many di erent criteria. Pavlidis [1] has proposed the following classi cati... |

257 | Fourier descriptors for plane closed curves
- Zahn, Roskies
- 1972
(Show Context)
Citation Context ...nal) and global (or internal), respectively. Examples of the former class are algorithms which parse the shape boundary [17, 18, 19, 20, 21, 22, 23, 24] and various Fourier transforms of the boundary =-=[25, 26, 27, 28, 29]-=-. Examples of global methods include the medial axis (also called symmetric axis) transform (MAT) proposed by Blum and described in [30, 31, 32, 17, 33, 34, 20, 22], moment based approaches [35, 36, 3... |

254 | Parts of recognition
- Hoffman, Richards
- 1984
(Show Context)
Citation Context ...e approximations. Stokely and Shang [93] investigated methods for measurement of the curvature of 3-D surfaces that evolve in many applications (e.g. tomographic medical images). Hoffman and Richards =-=[94, 95]-=- argue that when the visual system decomposes objects it does so at points of high negative curvature. This agrees with the principle of transversality [96] found in nature. The principle of transvers... |

249 |
Image analysis using mathematical morphology
- Haralick, Sternberg, et al.
- 1987
(Show Context)
Citation Context ...The authors demonstrated that the shape vector scheme can be used for shape matching. 5.3 Morphological Methods Mathematical morphology has evolved as a useful tool for various image processing tasks =-=[161, 162, 163, 164, 165]-=-. It is suitable for shape-related processing since morphological operations are directly related to the object shape. It is rst necessary to introduce some basic de nitions related to mathematical mo... |

239 |
Shape description using weighted symmetric axis features
- Blum, Nagel
- 1978
(Show Context)
Citation Context ... and various Fourier transforms of the boundary [25, 26, 27, 28, 29]. Examples of global methods include the medial axis (also called symmetric axis) transform (MAT) proposed by Blum and described in =-=[30, 31, 32, 17, 33, 34, 20, 22]-=-, moment based approaches [35, 36, 37, 38], and methods of shape decomposition into other primitive shapes [39, 40, 41, 42]. Another classi cation of shape analysis algorithms can be made on the basis... |

233 |
Human image understanding: Recent research and a theory
- Biederman
- 1985
(Show Context)
Citation Context ...An exhaustive survey of human visual perception research is beyond the scope of this paper. Some introductory and more advanced books and articles dealing with visual perception and cognition include =-=[4, 46, 47,48,49,50,51,52]-=-. In this section, a brief overview of visual perception research related to shape description is presented. 2.1 Classical Theories of Visual Perception Several schools of psychology have endeavored t... |

222 |
Image analysis via the general theory of moments
- Teague
- 1980
(Show Context)
Citation Context ...7, 28, 29]. Examples of global methods include the medial axis (also called symmetric axis) transform (MAT) proposed by Blum and described in [30, 31, 32, 17, 33, 34, 20, 22], moment based approaches =-=[35, 36, 37, 38]-=-, and methods of shape decomposition into other primitive shapes [39, 40, 41, 42]. Another classi cation of shape analysis algorithms can be made on the basis of whether the result of the analysis is ... |

219 |
Syntattic Pattern Recognition and Applications
- Fu
- 1982
(Show Context)
Citation Context ...the 17ssymmetry axis becomes more accurately determined. 4.2 Syntactic techniques Structural descriptions may be viewed as graphs and as such are suitable for formulation in terms of formal languages =-=[128, 129, 130, 131, 132]-=-. Syntactic methods have several important advantages. They attempt to emulate the structural and hierarchical nature of the HVS. Another advantage is that the theory of formal languages, which syntac... |

219 |
A theory of multiscale, curvature-based shape representation for planar curves
- Mokhtarian, Mackworth
- 1992
(Show Context)
Citation Context ...nctions of increasing width to obtain a multi-scale representation of shape boundary. The curvature is then computed at di erent scales to obtain the curvature primal sketch. Mokhtarian and Mackworth =-=[151, 152]-=- applied the scale-space approach to the description of planar shapes using the shape boundary. The curvature along the contour was next computed and smoothed with variable width Gaussian lters. The s... |

214 |
Distance transformations in arbitrary dimensions
- Borgefors
- 1984
(Show Context)
Citation Context ...nd a group was disquali ed if less then three consecutive segments matched. The nal step was used to measure the distance between two shapes. This was done by using the Chamfer 3=4 distance transform =-=[157, 158]-=- which approximates the Euclidean distance transform very well, but is less computationally intensive. The Chamfer 3=4 distance transform was computed for the 21srst boundary; the second boundary was ... |

204 |
efficiently computable metric for comparing polygonal shapes
- Arkin, Chew, et al.
- 1990
(Show Context)
Citation Context ...arc length function. The tangent angle at some point is measured relative to the tangent angle at the initial point. The function is also called the turning function and has been used by Arkin et al. =-=[108]-=- for comparing polygonal shapes. 11sO A4 A3 A2 A1 A0 Figure 1: The centroid-to-boundary distance approach. Granlund [26], Richards and Hemami [27], and Persoon and Fu [28] used a complex function of t... |

201 | The curvature primal sketch
- Asada, Brady
- 1986
(Show Context)
Citation Context ...width of the lter is increased. In other words, contours in scale-space image cannot disappear when the lter width is increased. The Gaussian lter is the only lter with such property. Asada and Brady =-=[150]-=- proposed a new approach based on the ideas developed by Marr et al. to introduce 20sa representation called the curvature primal sketch. This is a scale-space approach for the representation of curva... |

200 |
Shape discrimination using fourier descriptors
- Persoon, Fu
- 1986
(Show Context)
Citation Context ...nal) and global (or internal), respectively. Examples of the former class are algorithms which parse the shape boundary [17, 18, 19, 20, 21, 22, 23, 24] and various Fourier transforms of the boundary =-=[25, 26, 27, 28, 29]-=-. Examples of global methods include the medial axis (also called symmetric axis) transform (MAT) proposed by Blum and described in [30, 31, 32, 17, 33, 34, 20, 22], moment based approaches [35, 36, 3... |

197 |
Symbolic reasoning among 3-D models and 2-D images
- Brooks
- 1981
(Show Context)
Citation Context ...e selection to only skeleton points. The generalized skeleton has proven to have better noise robustness [33]. The concept of symmetry and symmetric axis has been further developed in works by Brooks =-=[195]-=- and Brady [45]. The problem of determining the axis of symmetry is related to an inverse problem - the generation of shapes from their symmetric axis. Objects generated in such a way are called ribbo... |

194 |
On encoding arbitrary geometric configurations
- Freeman
- 1961
(Show Context)
Citation Context ...2 13 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 A 14 Figure 3: The generalized chain code. in the following subsections. 4.1 Chain Code Freeman =-=[123]-=- has proposed a method for coding line drawings called chain coding. A more detailed overview of chain code methods and algorithms by Freeman can be found in [124]. The generalized chain code [125] is... |

193 |
Sequential operations in digital picture processing
- Rosenfeld, Pfaltz
- 1966
(Show Context)
Citation Context ...e must position a disk of radius q(x) at location x, for each x 2 S. The union of all disks is equal to the original shape. Wave front propagation can be computed using the distance transform methods =-=[182, 183]-=- or the shrinking operation [31]. Gray scale images have been processed using the min-max operators [184, 34, 185]. The shrinking and related Boolean-nature local neighborhood operators have been used... |

185 |
Computer processing of line-drawing images
- Freeman
- 1974
(Show Context)
Citation Context ... The generalized chain code. Freeman [123] has proposed a method for coding line drawings called chain coding. A more detailed overview of chain code methods and algorithms by Freeman can be found in =-=[124]-=-. The generalized chain code [125] is shown in Figure 3. The nodes surrounding node A are enumerated counter-clockwise in ascending order from inside out. The link ai is a directed line segment. A cha... |

182 | Scale-based description and recognition of planar curves and two-dimensional shapes
- Mokhtarian, Mackworth
- 1986
(Show Context)
Citation Context ...nctions of increasing width to obtain a multi-scale representation of shape boundary. The curvature is then computed at di erent scales to obtain the curvature primal sketch. Mokhtarian and Mackworth =-=[151, 152]-=- applied the scale-space approach to the description of planar shapes using the shape boundary. The curvature along the contour was next computed and smoothed with variable width Gaussian lters. The s... |