## Planar Grouping for Automatic Detection of Vanishing Lines and Points (2000)

Venue: | Image and Vision Computing |

Citations: | 34 - 1 self |

### BibTeX

@ARTICLE{Schaffalitzky00planargrouping,

author = {Frederik Schaffalitzky and Andrew Zisserman},

title = {Planar Grouping for Automatic Detection of Vanishing Lines and Points},

journal = {Image and Vision Computing},

year = {2000},

volume = {18},

pages = {647--658}

}

### Years of Citing Articles

### OpenURL

### Abstract

It is demonstrated that grouping together features which satisfy a geometric relationship can be used both for (automatic) detection and estimation of vanishing points and lines. We describe the geometry of three commonly occurring types of geometric grouping and present efficient grouping algorithms which exploit these geometries. The three types of grouping are : (1) a family of equally spaced coplanar parallel lines, (2) a planar pattern obtained by repeating some element by translation in the plane, and (3) a set of elements arranged in a regular planar grid. Examples of automatically computing groupings, together with their vanishing points and lines, are given for a number of real images. Key words: Grouping, Vanishing Point and Line Detection, Repetition. 1 Introduction Suppose a plane in the world is imaged by a perspective camera. Then the line at infinity of the plane is projected to a line in the image, the vanishing line. The objective of this paper is to automatically e...

### Citations

3265 | A computational approach to edge detection
- Canny
- 1986
(Show Context)
Citation Context ...e original RANSAC sample. As new lines are included the MLE of A is recomputed. 3.1.3 Algorithm summary and results In summary the full algorithm has the following stages : (1) Line detection. (Canny =-=[2]-=-) edge detection and segmentation into straight lines by breaking edges at points of high curvature. 11 (2) Group concurrent lines. RANSAC is used to search for concurrent line within the detected lin... |

2609 |
Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography
- Fischler, Bolles
- 1981
(Show Context)
Citation Context ...int detection; the second stage then uses the relations of section 2.2 to select coplanar equally spaced parallel scene lines from the concurrent line sets. 3.1.1 Grouping concurrent lines The RANSAC =-=[7]-=- robust estimation algorithm is used to search for concurrent lines amongst the detected line segments. In brief, RANSAC is an algorithm which simultaneously fits parameters and rejects outliers. The ... |

1813 | A Combined Corner and Edge Detector
- Harris, Stephens
- 1988
(Show Context)
Citation Context ...ven for features consisting of interest points, though of course it may be applied to other feature types. (1) RANSAC search for 1D collinear repetitions. (a) Interest point detection (Harris corners =-=[9]-=-). (b) Grouping together of nearby interest points whose intensity neighbourhoods have correlation coefficient above 0:80. Each of the resulting groupings are fed separately to the subsequent stages. ... |

1302 |
Three-Dimensional Computer Vision: A Geometric Viewpoint
- Faugeras
- 1993
(Show Context)
Citation Context .... Lines in IP 2 are described by their vector of coefficients, for example the line ax+by+c = 0 is represented as l = (a; b; c) ? . A perspective camera P is modelled as a 3 \Theta 4 matrix of rank 3 =-=[6]-=-. As a result [15], the mapping (figure 2) from world plane to image plane is described by a 3 \Theta 3 matrix M, dependent on the particular coordinates used on the world and image planes. Such a tra... |

237 |
Geometric invariance in computer vision
- Mundy, Zisserman
- 1992
(Show Context)
Citation Context ...re described by their vector of coefficients, for example the line ax+by+c = 0 is represented as l = (a; b; c) ? . A perspective camera P is modelled as a 3 \Theta 4 matrix of rank 3 [6]. As a result =-=[15]-=-, the mapping (figure 2) from world plane to image plane is described by a 3 \Theta 3 matrix M, dependent on the particular coordinates used on the world and image planes. Such a transformation is a p... |

206 |
Algebraic projective geometry
- Semple, Kneebone
- 1952
(Show Context)
Citation Context ...homography Homogeneous coordinates (x; w) ? , (x; y; w) ? and (x; y; z; w) ? are used for points on the projective line IP 1 , on the projective plane IP 2 and in projective space IP 3 , respectively =-=[20]-=-. Lines in IP 2 are described by their vector of coefficients, for example the line ax+by+c = 0 is represented as l = (a; b; c) ? . A perspective camera P is modelled as a 3 \Theta 4 matrix of rank 3 ... |

155 | Finding naked people
- Fleck, Forsyth, et al.
- 1996
(Show Context)
Citation Context ...s can be carried out efficiently even in the presence of multiple groupings and clutter features. The response of a grouping algorithm indicates the likely presence or absence of an object in a scene =-=[8,25]-=-. In our case, the response of any of the groupers that we presented is evidence for the presence of things like buildings, zebra crossings [24] and brick walls. Such groupings define a feature that m... |

138 | Wide baseline stereo matching
- Pritchett, Zisserman
- 1998
(Show Context)
Citation Context ...only affine rather than projective [4]; second, the grouping provides an affine invariant feature. Such a feature may be used for matching between images, for example in wide baseline stereo matching =-=[17]-=-, or between an image and an image database, for example in image retrieval or object recognition. 2 O x X Image plane World plane Y y x = MX y = PY Fig. 2. A perspective camera P induces a plane-to-p... |

131 | Metric rectification for perspective images of planes
- Liebowitz, Zisserman
- 1998
(Show Context)
Citation Context ...g Hough transforms (clustering) or other robust methods (see, for example [1,3,13,14,21,23,18] where earlier references are given) and also the estimation of vanishing points given a cluster of lines =-=[5,12,14]-=-. The novelty of the work presented here is in employing the additional constraints that arise from structured groupings of parallel elements on planes. To motivate the approach consider the bars of t... |

68 | Vanishing point calculation as a statistical inference on the unit sphere
- Collins, Weiss
- 1990
(Show Context)
Citation Context ...g Hough transforms (clustering) or other robust methods (see, for example [1,3,13,14,21,23,18] where earlier references are given) and also the estimation of vanishing points given a cluster of lines =-=[5,12,14]-=-. The novelty of the work presented here is in employing the additional constraints that arise from structured groupings of parallel elements on planes. To motivate the approach consider the bars of t... |

53 |
Determination of vanishing points using hough transform
- Lutton, Maitre, et al.
- 1994
(Show Context)
Citation Context ...vanishing line from the image. Much previous research has addressed the automatic detection of vanishing points and lines using Hough transforms (clustering) or other robust methods (see, for example =-=[1,3,13,14,21,23,18]-=- where earlier references are given) and also the estimation of vanishing points given a cluster of lines [5,12,14]. The novelty of the work presented here is in employing the additional constraints t... |

51 | Detecting, localizing and grouping repeated scene elements from an image
- Leung, Malik
- 1996
(Show Context)
Citation Context ... This is four less degrees of freedom than a general homography, and two less than the canonical and `simple' affine transformation used by many authors in the past for this type of imaged repetition =-=[11]-=-, --- yet the transformation H exactly models perspective effects which are not accounted for by an affine transformation. The parameters of the elation may be computed from two point correspondences,... |

43 |
Geometry and Analysis of Projective Spaces
- Springer
- 1964
(Show Context)
Citation Context ...ons of the parameters are illustrated in figure 6. Since v lies on l 1 it satisfies l ? 1 v = 0. An image transformation of this form (ie. of the form I+vl ? 1 where l ? 1 v = 0) is called an elation =-=[20,22]-=-. This class of transformations has only 4 degrees of freedom, which are specified 6 l H v Fig. 6. Left, geometric interpretation of the parameters of a conjugate translation. Right, example of elatio... |

42 |
Determining perspective structures using hierarchical Hough transform
- Quan, Mohr
- 1989
(Show Context)
Citation Context ...vanishing line from the image. Much previous research has addressed the automatic detection of vanishing points and lines using Hough transforms (clustering) or other robust methods (see, for example =-=[1,3,13,14,21,23,18]-=- where earlier references are given) and also the estimation of vanishing points given a cluster of lines [5,12,14]. The novelty of the work presented here is in employing the additional constraints t... |

37 | Geometric grouping of repeated elements within images
- Schaffalitzky, Zisserman
- 1999
(Show Context)
Citation Context ...eap) to search the set of image features for more correspondences because the elation predicts the location of the correspondent of a given feature. This algorithm is also described in more detail in =-=[19]-=-. Figures 16 and 17 show examples of groupings and vanishing lines computed by this algorithm. 3.3 Regular grid of repetitions on a plane The objective here is to detect and group image features which... |

33 |
Vanishing point detection by line clustering
- McLean, Kotturi
- 1995
(Show Context)
Citation Context ...vanishing line from the image. Much previous research has addressed the automatic detection of vanishing points and lines using Hough transforms (clustering) or other robust methods (see, for example =-=[1,3,13,14,21,23,18]-=- where earlier references are given) and also the estimation of vanishing points given a cluster of lines [5,12,14]. The novelty of the work presented here is in employing the additional constraints t... |

26 |
New Method for Vanishing Point Detection
- Brillault-Oâ€™Mahony
- 1991
(Show Context)
Citation Context |

25 | S.: Class-based grouping in perspective images
- Zisserman, Mundy, et al.
- 1995
(Show Context)
Citation Context ...s can be carried out efficiently even in the presence of multiple groupings and clutter features. The response of a grouping algorithm indicates the likely presence or absence of an object in a scene =-=[8,25]-=-. In our case, the response of any of the groupers that we presented is evidence for the presence of things like buildings, zebra crossings [24] and brick walls. Such groupings define a feature that m... |

24 |
Minimizing algebraic error in geometric estimation problems
- Hartley
- 1998
(Show Context)
Citation Context ...on the line data first: for example, the image or region containing the lines can be transformed to fill the inside of the unit square. The matrix is then computed using a linear algorithm similar to =-=[10]-=-: each correspondence imposes linear constraints on the entries of A. The resulting linear system, which may be overconstrained, can be solved by singular value decomposition. 10 Now, while it is true... |

19 | Matching perspective views of coplanar structures using projective unwarping and similarity matching
- Collins, Beveridge
- 1993
(Show Context)
Citation Context ...ng line is obtained the affine properties of the plane are determined. The complexity of any subsequent matching operation is then reduced because the distortion is only affine rather than projective =-=[4]-=-; second, the grouping provides an affine invariant feature. Such a feature may be used for matching between images, for example in wide baseline stereo matching [17], or between an image and an image... |

18 | The Cascaded Hough Transform as an Aid in Aerial Image Interpretation
- Tuytelaars, Gool, et al.
- 1998
(Show Context)
Citation Context |

18 | Grouping based on projective geometry constraints and uncertainty
- Utcke
- 1998
(Show Context)
Citation Context ...he likely presence or absence of an object in a scene [8,25]. In our case, the response of any of the groupers that we presented is evidence for the presence of things like buildings, zebra crossings =-=[24]-=- and brick walls. Such groupings define a feature that may be used as the basis for further tasks such as image matching, and this is the subject of current work. Acknowledgements The algorithms in th... |

5 |
Performance and analysis of vanishing point detection techniques
- Shufelt
- 1999
(Show Context)
Citation Context |

4 |
Using Geometrical Rules and a Priori Knowledge for Understanding of Indoor Scenes
- Straforini, Coelho, et al.
- 1990
(Show Context)
Citation Context |