Detect points of interest using the Förstner operator.

points_foerstner extracts significant points from an image. Significant points are points that differ from their neighborhood, i.e., points where the image function changes in two dimensions. These changes occur on the one hand at the intersection of image edges (called junction points), and on the other hand at places where color or brightness differs from the surrounding neighborhood (called area points).

The point extraction takes place in two steps: In the first step the point regions, i.e., the inhomogeneous, isotropic regions, are extracted from the image. To do so, the smoothed matrix

        /   n                n              \
        |  ---              ---             |
        |  \        2       \               |
        |  /    Ix,c        /    Ix,c Iy,c  |
        |  ---              ---             |
        |  c=1              c=1             |
M = S * |                                   |
        |   n                n              |
        |  ---              ---             |
        |  \                \        2      |
        |  /    Ix,c Iy,c   /    Iy,c       |
        |  ---              ---             |
        \  c=1              c=1             /

inhomogeneity = Trace(M)

                    Det(M)
isotropy = 4 * -----------------
               Trace(M)*Trace(M)

In the second step, two optimization functions are calculated for the resulting points. Essentially, these optimization functions average for each point the distances to the edge directions (for junction points) and the gradient directions (for area points) within an observation window around the point. If Smoothing is 'gauss', the averaging is performed by a Gaussian of size SigmaPoints, if Smoothing is 'mean', the averaging is performed by a SigmaPoints x SigmaPoints mean filter. The local minima of the optimization functions determine the extracted points. Their subpixel precise position is returned in (RowJunctions, ColJunctions) and (RowArea, ColArea).

In addition to their position, for each extracted point the elements CoRRJunctions, CoRCJunctions, and CoCCJunctions (and CoRRArea, CoRCArea, and CoCCArea, respectively) of the corresponding covariance matrix are returned. This matrix facilitates conclusions about the precision of the calculated point position. To obtain the actual values, it is necessary to estimate the amount of noise in the input image and to multiply all components of the covariance matrix with the variance of the noise. (To estimate the amount of noise, apply intensity to homgeneous image regions or plane_deviation to image regions, where the gray values form a plane. In both cases the amount of noise is returned in the parameter Deviation.) This is illustrated by the example program

%HALCONROOT%\examples\hdevelop\Filter\Points\points_foerstner_ellipses.dev

It lies in the nature of this operator that corners often result in two distinct points: One junction point, where the edges of the corner actually meet, and one area point inside the corner. Such doublets will be eliminated automatically, if EliminateDoublets is 'true'. To do so, each pair of one junction point and one area point is examined. If the points lie within each others' observation window of the optimization function, for both points the precision of the point position is calculated and the point with the lower precision is rejected. If EliminateDoublets is 'false', every detected point is returned.

Note that only odd values for SigmaInt and SigmaPoints are allowed, if Smoothing is 'mean'. Even values automatically will be replaced by the next larger odd value.

points_foerstner returns 2 (H_MSG_TRUE) if all parameters are correct and no error occurs during the execution. If the input is empty the behavior can be set via set_system('no_object_result',<Result>). If necessary, an exception handling is raised.

points_foerstner is reentrant and processed without parallelization.

gen_cross_contour_xld, disp_cross

points_harris

W. Förstner, E. Gülch: ``A Fast Operator for Detection and Precise Location of Distinct Points, Corners and Circular features''. In Proceedings of the Intercommission Conference on Fast Processing of Photogrametric Data, Interlaken, pp. 281-305, 1987.

W. Förstner: ``Statistische Verfahren für die automatische Bildanalyse und ihre Bewertung bei der Objekterkennung und -vermessung''. Volume 370, Series C, Deutsche Geodätische Kommission, München, 1991.

W. Förstner: ``A Framework for Low Level Feature Extraction''. European Conference on Computer Vision, LNCS 802, pp. 383-394, Springer Verlag, 1994.

C. Fuchs: ``Extraktion polymorpher Bildstrukturen und ihre topologische und geometrische Gruppierung''. Volume 502, Series C, Deutsche Geodätische Kommission, München, 1998.

Foundation