## A Computational Approach for Corner and Vertex Detection (1992)

Venue: | International Journal of Computer Vision |

Citations: | 107 - 1 self |

### BibTeX

@ARTICLE{Deriche92acomputational,

author = {Rachid Deriche and Gerard Giraudon},

title = {A Computational Approach for Corner and Vertex Detection},

journal = {International Journal of Computer Vision},

year = {1992},

volume = {10},

pages = {101--124}

}

### OpenURL

### Abstract

Corners and vertices are strong and useful features in Computer Vision for scene analysis, stereo matching and motion analysis. This paper deals with the development of a computational approach to these important features. We consider first a corner model and study analytically its behavior once it has been smoothed using the well-known Gaussian filter. This allows us to clarify the behavior of some well known cornerness measure based approaches used to detect these points of interest. Most of these classical approaches appear to detect points that do not correspond to the exact position of the corner. A new scale-space based approach that combines useful properties from the Laplacian and Beaudet's measure [Bea78] is then proposed in order to correct and detect exactly the corner position. An extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection. In particular, it is shown that a trihedral vertex has two elliptic maxima on ...

### Citations

1731 | A Combined Corner and Edge Detector
- Harris, Stephens
- 1988
(Show Context)
Citation Context ...proach in order to detect corners and vertices. See the work of Dreschler and Nagel [Dre82a], [Nag83a], Kitchen and Rosenfeld [Kit82] and, more recently, the work of Noble [Nob88], Harris and Stephen =-=[Har88]-=-, Singh [Sin90], Rangarajan [Ran89], Guidicci [Gui88], Deriche and Giraudon [Der90], [Gir90], Beymer [Bey89] and Rohr [Roh90]. This paper deals with the second type of approach. We develop a computati... |

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- 1980
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- 1986
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Citation Context ...n the last few years. They can be broadly divided into two groups : Approaches in the first group involve first extracting edges as a chain code, and then searching for points having maxima curvature =-=[Asa86]-=-, [Der90], [Med86] or performing a polygonal approximation on the chains and then searching for the line segment intersections [Hor90]. The second group consists of approaches that work directly on a ... |

186 |
Towards automatic visual obstacle avoidance
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- 1977
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- 1986
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Citation Context ...e isolated corners using a non maximum suppression process applied on the gradient magnitude before its multiplication with the curvature. In fact, it can be shown (see, for example, Torre and Poggio =-=[Tor86]-=-) that K is the explicit representation for the second directional derivative in the direction orthogonal to the gradient. Nagel [Nag83a] has shown that Dreschel-Nagel's approach and Kitchen-Rosenfeld... |

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Citation Context ...at affects all the previous approaches. 6 Harris and Stephen [Har88] considered a slightly modified version of the Plessey corner detector. From Moravec's work [Mor77] and Barnard and Thompson's work =-=[Bar80]-=-, they define a measure based on the following operator: R(x; y) = Det[sC] \Gamma kTrace 2 [sC] (10) Harris gives a value of k equal to 0.04 for providing discrimination against high contrast pixel st... |

123 |
Gray-level corner detection
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- 1982
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Citation Context ...surface. A great deal of effort has been devoted to this second type of approach in order to detect corners and vertices. See the work of Dreschler and Nagel [Dre82a], [Nag83a], Kitchen and Rosenfeld =-=[Kit82]-=- and, more recently, the work of Noble [Nob88], Harris and Stephen [Har88], Singh [Sin90], Rangarajan [Ran89], Guidicci [Gui88], Deriche and Giraudon [Der90], [Gir90], Beymer [Bey89] and Rohr [Roh90].... |

111 |
Displacement vectors derived from second-order intensity variations in image sequences
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- 1983
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Citation Context ...ts and of the curvatures of the surface. A great deal of effort has been devoted to this second type of approach in order to detect corners and vertices. See the work of Dreschler and Nagel [Dre82a], =-=[Nag83a]-=-, Kitchen and Rosenfeld [Kit82] and, more recently, the work of Noble [Nob88], Harris and Stephen [Har88], Singh [Sin90], Rangarajan [Ran89], Guidicci [Gui88], Deriche and Giraudon [Der90], [Gir90], B... |

108 | Edge focusing - Bergholm - 1987 |

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Rotationally invariant image operators
- Beaudet
- 1978
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Citation Context ...pproaches appear to detect points that do not correspond to the exact position of the corner. A new scale-space based approach that combines useful properties from the Laplacian and Beaudet's measure =-=[Bea78]-=- is then proposed in order to correct and detect exactly the corner position. An extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection. I... |

77 | Volumetric model and 3D trajectory of a moving car derived from monocular TV-frame sequence of a street scene - Dreschler, Nagel - 1982 |

60 | Finding Corners
- Noble
- 1988
(Show Context)
Citation Context ...ed to this second type of approach in order to detect corners and vertices. See the work of Dreschler and Nagel [Dre82a], [Nag83a], Kitchen and Rosenfeld [Kit82] and, more recently, the work of Noble =-=[Nob88]-=-, Harris and Stephen [Har88], Singh [Sin90], Rangarajan [Ran89], Guidicci [Gui88], Deriche and Giraudon [Der90], [Gir90], Beymer [Bey89] and Rohr [Roh90]. This paper deals with the second type of appr... |

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Corner detection and curve representation using cubic b-splines
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- 1987
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Citation Context ...rs. They can be broadly divided into two groups : Approaches in the first group involve first extracting edges as a chain code, and then searching for points having maxima curvature [Asa86], [Der90], =-=[Med86]-=- or performing a polygonal approximation on the chains and then searching for the line segment intersections [Hor90]. The second group consists of approaches that work directly on a grey-level image. ... |

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Accurate corner detection: An analytical study
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Citation Context ...t few years. They can be broadly divided into two groups : Approaches in the first group involve first extracting edges as a chain code, and then searching for points having maxima curvature [Asa86], =-=[Der90]-=-, [Med86] or performing a polygonal approximation on the chains and then searching for the line segment intersections [Hor90]. The second group consists of approaches that work directly on a grey-leve... |

39 |
Corner detection using the facet model
- Zuniga, Haralick
- 1983
(Show Context)
Citation Context ... are then obtained by thresholding. Among the most popular corner detectors are those proposed by Beaudet [Bea78], Dreschler and Nagel [Dre82a], Kitchen and Rosenfeld [Kit82], and Zuniga and Haralick =-=[Zun83]-=-. In fact, it has been reported by Nagel [Nag83a] and by Shah and Jain [Sha84] that the three last detectors are equivalent. We will show that these detectors do not detect the exact position of a cor... |

38 | Constraints for the estimation of displacement vector fields from image sequences - Nagel - 1983 |

37 | Determination of ego-motion from matched points
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Citation Context ...itude. Recently, Noble [Nob88] tried to give a theoretical formulation for the corner detection problem using differential geometry. She outlined the principles underlying the Plessey corner detector =-=[Har87], whi-=-ch is based only on first differentials : C p = Trace( C) Det(sC) (7) where C is the following matrix :sC = " I 2 xsI x I y I x I y I 2 y # (8) and where I denotes the smoothing operation on I . ... |

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Optimal Edge Detection Using Recursive Filtering
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Citation Context ...munity on this problem, and in particular on the problem of edge detection, where an extensive literature has been developed from Marr and Hildreth's work [Mar80] to Canny and Deriche's work [Can86], =-=[Der87]-=-. Corners and vertices as features are very important and represent another class of relevant information in computer vision. These features can be used to identify objects in the scene, for stereosco... |

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Accuracy of Laplacian Edge Detectors
- Berzins
- 1984
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Citation Context ... of the paper. Let g(x) denote the zero mean Gaussian filter : g(x) = 1 p 2 e \Gamma x 2 2 (11) The two-dimensional Gaussian filter G can be expressed as : G(x; y) = g(x)g(y) (12) 7 Following Berzins =-=[Ber84]-=-, we work in a coordinate system where the unit length is equal to the scale factor oe of the filter. In order to convert the results into a more general coordinate system (X; Y ), we use the followin... |

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Diā¬erential geometry
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Citation Context ...act, this operator can be interpretated as the Hessian determinant, H = " I xx I xy I yx I yy # (2) which is related to the product of the principal curvaturessminsmax , called the Gaussian Curva=-=ture [Lip69]-=- as follows : ( min max ) = DET (1 + I 2 x + I 2 y ) 2 (3) In terms of differential geometry, we can say that for a pixel I(x; y), Ifsmin max ? 0 () the pixel is an elliptic point Ifsmin max ! 0 () th... |

18 |
On the selection of critical points and local curvature extrema of region boundaries for interframe matching
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- 1982
(Show Context)
Citation Context ...he gradients and of the curvatures of the surface. A great deal of effort has been devoted to this second type of approach in order to detect corners and vertices. See the work of Dreschler and Nagel =-=[Dre82a]-=-, [Nag83a], Kitchen and Rosenfeld [Kit82] and, more recently, the work of Noble [Nob88], Harris and Stephen [Har88], Singh [Sin90], Rangarajan [Ran89], Guidicci [Gui88], Deriche and Giraudon [Der90], ... |

16 |
Localisation and Noise in Edge Detection
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- 1989
(Show Context)
Citation Context ...valent. We will show that these detectors do not detect the exact position of a corner. A more recent approach is the one developed by Harris and Stephens [Har88] and Noble [Nob88]. De Michelli et al =-=[Mic89]-=- present a comparative study between zero-crossing and gradient approaches on corner and trihedral vertex detection. Their scheme does not correctly detect corners or vertices. However, they have alre... |

14 |
level corner detection a generalization and a robust real time implementation
- Singh, Shneier, et al.
- 1990
(Show Context)
Citation Context ... to detect corners and vertices. See the work of Dreschler and Nagel [Dre82a], [Nag83a], Kitchen and Rosenfeld [Kit82] and, more recently, the work of Noble [Nob88], Harris and Stephen [Har88], Singh =-=[Sin90]-=-, Rangarajan [Ran89], Guidicci [Gui88], Deriche and Giraudon [Der90], [Gir90], Beymer [Bey89] and Rohr [Roh90]. This paper deals with the second type of approach. We develop a computational approach t... |

13 |
Optimal corner detector
- Rangarajan, Shah, et al.
- 1989
(Show Context)
Citation Context ...nd vertices. See the work of Dreschler and Nagel [Dre82a], [Nag83a], Kitchen and Rosenfeld [Kit82] and, more recently, the work of Noble [Nob88], Harris and Stephen [Har88], Singh [Sin90], Rangarajan =-=[Ran89]-=-, Guidicci [Gui88], Deriche and Giraudon [Der90], [Gir90], Beymer [Bey89] and Rohr [Roh90]. This paper deals with the second type of approach. We develop a computational approach that allows us to ana... |

9 |
Corner characterization by differential geometry techniques
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- 1988
(Show Context)
Citation Context ...he work of Dreschler and Nagel [Dre82a], [Nag83a], Kitchen and Rosenfeld [Kit82] and, more recently, the work of Noble [Nob88], Harris and Stephen [Har88], Singh [Sin90], Rangarajan [Ran89], Guidicci =-=[Gui88]-=-, Deriche and Giraudon [Der90], [Gir90], Beymer [Bey89] and Rohr [Roh90]. This paper deals with the second type of approach. We develop a computational approach that allows us to analytically study a ... |

8 |
Detecting Time-Varying Corners
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- 1984
(Show Context)
Citation Context ...e those proposed by Beaudet [Bea78], Dreschler and Nagel [Dre82a], Kitchen and Rosenfeld [Kit82], and Zuniga and Haralick [Zun83]. In fact, it has been reported by Nagel [Nag83a] and by Shah and Jain =-=[Sha84]-=- that the three last detectors are equivalent. We will show that these detectors do not detect the exact position of a corner. A more recent approach is the one developed by Harris and Stephens [Har88... |

4 |
The geometry of differential operators with application to image processing
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- 1989
(Show Context)
Citation Context ...on of hyperbolic extrema is exactly the localization of corner. We refer the reader who is interested in other kinds of approaches to the following references : [Hua86], [Ran89], [Sin90], [Roh90] and =-=[Kru89]-=-. 3 An Analytical Study of the Corner Model In this section, we consider a corner model and study its behavior in the scale space. This allows us to derive results that completely clarify the behavior... |

2 |
T.SKORDAS:"Finding Geometric and Relational Structures in an Image
- VEILLON
- 1990
(Show Context)
Citation Context ...chain code, and then searching for points having maxima curvature [Asa86], [Der90], [Med86] or performing a polygonal approximation on the chains and then searching for the line segment intersections =-=[Hor90]-=-. The second group consists of approaches that work directly on a grey-level image. Several techniques have been proposed within this group. These techniques are based either on heuristic techniques l... |

1 |
BEYMER "Junctions : Their detection and use for grouping in images
- J
- 1989
(Show Context)
Citation Context ...hen and Rosenfeld [Kit82] and, more recently, the work of Noble [Nob88], Harris and Stephen [Har88], Singh [Sin90], Rangarajan [Ran89], Guidicci [Gui88], Deriche and Giraudon [Der90], [Gir90], Beymer =-=[Bey89]-=- and Rohr [Roh90]. This paper deals with the second type of approach. We develop a computational approach that allows us to analytically study a corner and a trihedral vertex model. This allows us to ... |

1 |
A Computational Approch to Edge Detection
- CANNY
- 1986
(Show Context)
Citation Context ...ision community on this problem, and in particular on the problem of edge detection, where an extensive literature has been developed from Marr and Hildreth's work [Mar80] to Canny and Deriche's work =-=[Can86]-=-, [Der87]. Corners and vertices as features are very important and represent another class of relevant information in computer vision. These features can be used to identify objects in the scene, for ... |

1 |
FAUGERAS: "2-D Curve Matching Using High Curvature Points: Application to Stereo Vision
- DERICHE, D
- 1990
(Show Context)
Citation Context ...t few years. They can be broadly divided into two groups : Approaches in the first group involve first extracting edges as a chain code, and then searching for points having maxima curvature [Asa86], =-=[Der90]-=-, [Med86] or performing a polygonal approximation on the chains and then searching for the line segment intersections [Hor90]. The second group consists of approaches that work directly on a grey-leve... |

1 |
and R.DERICHE : "On Corner and Vertex Detection
- GIRAUDON
- 1991
(Show Context)
Citation Context ..., [Nag83a], Kitchen and Rosenfeld [Kit82] and, more recently, the work of Noble [Nob88], Harris and Stephen [Har88], Singh [Sin90], Rangarajan [Ran89], Guidicci [Gui88], Deriche and Giraudon [Der90], =-=[Gir90]-=-, Beymer [Bey89] and Rohr [Roh90]. This paper deals with the second type of approach. We develop a computational approach that allows us to analytically study a corner and a trihedral vertex model. Th... |

1 |
A direct corner detection algorithm
- HUA, QUIAN
- 1986
(Show Context)
Citation Context ...side the corner. For ` = =2, the location of hyperbolic extrema is exactly the localization of corner. We refer the reader who is interested in other kinds of approaches to the following references : =-=[Hua86]-=-, [Ran89], [Sin90], [Roh90] and [Kru89]. 3 An Analytical Study of the Corner Model In this section, we consider a corner model and study its behavior in the scale space. This allows us to derive resul... |

1 |
Uber die Modellierung and Identifikation charakteristischer Grauwertverlaufe
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- 1990
(Show Context)
Citation Context ... [Kit82] and, more recently, the work of Noble [Nob88], Harris and Stephen [Har88], Singh [Sin90], Rangarajan [Ran89], Guidicci [Gui88], Deriche and Giraudon [Der90], [Gir90], Beymer [Bey89] and Rohr =-=[Roh90]-=-. This paper deals with the second type of approach. We develop a computational approach that allows us to analytically study a corner and a trihedral vertex model. This allows us to clarify the behav... |