Vanishing Point Detection

Objectives:

Vanishing points are points in the image plane in which lines, that are parallel in object space, intersect. A vanishing point can be located within or outside the image itself, or even at infinity (see the first image of the example below).

Three vanishing points in an image of a building

The procedure described here, starts with automatically extracted straight image lines and clusters the lines that intersect in a vanishing point. With the detection of (the lines that constitute) a vanishing point, the orientation of the lines - relative to the co-ordinate system of the camera - is known. If three vanishing points are detected of which the object orientations are assumed to be perpendicular, it is often possible to estimate camera parameters such as the focal length.
So, vanishing point detection can be applied in these basic photogrammetric tasks:

Object reconstruction
Exterior orientation (pose estimation)
Camera calibration

Approach:

Detection of three perpendicular vanishing points
:

(object orientations of the lines associated with the vanishing points are assumed to be perpendicular)

Extraction of straight lines using a line-growing algoritm, possibly after correction of the image for lensdistortions
Selection of longest line ("start" line), assuming it is a line of a vanishing point
Computation of statistical tests of the hypothesis of intersection of 2 lines and the "start" line (O(n²) tests; n lines)
Clustering of lines based on the statistical testing results; the lines of the largest cluster intersect in the first vanishing point
Due to the perpendicularity assumption, the first vanishing point can be used instead of the "start" line for the statistical tests for the detection of the second vanishing point (again O(n²) tests).
With the perpendicularity of the third vanishing point relative to the previous two, the detection of the third vanishing point requires only O(n) statistical tests.

Validation by least-squares adjustment and testing
In a final least-squares adjustment all parallelism and perpendicularity conditions are used for a validation of the vanishing point detection. Lines that are clustered to more than one vanishing point are excluded. These lines connect vanishing points and are called horizon lines (see the example below). The use of the perpendicularity assumptions (and the use of the "start" line for the detection of the first vanishing point) reduce the computational burden considerably. Furthermore, the example shows that the approach allows the detection of even a single line of the third vanishing point (after elimination of horizon lines).

Example:

The lines of the three vanishing points of an image of the Geodesy building:

Lines of first vanishing point.

Lines of second vanishing point.

Lines of third vanishing point.

Lines not associated with a vanishing point

Lines adjusted in an overall adjustment (horizon lines are eliminated).

Lines not in the overall adjustment (non-vanishing point and horizon lines).

Publication:

F.A. van den Heuvel, 1998.

Vanishing point detection for architectural photogrammetry
International Archives of Photogrammetry and Remote Sensing, Vol. XXXII part 5, pp.652-659

(download the pdf file; 0.8Mb)