Operators

# points_foerstner (Operator)

## Name

points_foerstner — Detect points of interest using the Förstner operator.

## Signature

points_foerstner(Image : : SigmaGrad, SigmaInt, SigmaPoints, ThreshInhom, ThreshShape, Smoothing, EliminateDoublets : RowJunctions, ColumnJunctions, CoRRJunctions, CoRCJunctions, CoCCJunctions, RowArea, ColumnArea, CoRRArea, CoRCArea, CoCCArea)

## Description

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

is calculated, where and are the first derivatives of each image channel and S stands for a smoothing. If Smoothing is 'gauss', the derivatives are computed with Gaussian derivatives of size SigmaGrad and the smoothing is performed by a Gaussian of size SigmaInt. If Smoothing is 'mean', the derivatives are computed with a 3 x 3 Sobel filter (and hence SigmaGrad is ignored) and the smoothing is performed by a SigmaInt x SigmaInt mean filter. Then
inhomogeneity = Trace(M)
is the degree of inhomogeneity in the image and
is the degree of the isotropy of the texture in the image. Image points that have an inhomogeneity greater or equal to ThreshInhom and at the same time an isotropy greater or equal to ThreshShape are subsequently examined further.

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, ColumnJunctions) and (RowArea, ColumnArea).

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 homogeneous 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

%HALCONEXAMPLES%\hdevelop\Filter\Points\points_foerstner_ellipses.hdev
.

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.

## Attention

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 with Smoothing = 'gauss' uses a special implementation that is optimized using SSE2 instructions if the system parameter 'sse2_enable' is set to 'true' (which is default if SSE2 is available on your machine). This implementation is slightly inaccurate compared to the pure C version due to numerical issues (for 'byte' images the difference in RowJunctions and ColumnJunctions is in order of magnitude of 1.0e-5). If you prefer accuracy over performance you can set 'sse2_enable' to 'false' (using set_system) before you call points_foerstner. This way points_foerstner does not use SSE2 accelerations. Don't forget to set 'sse2_enable' back to 'true' afterwards.

Note that filter operators may return unexpected results if an image with a reduced domain is used as input. Please refer to the chapter Filters.

## Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Automatically parallelized on internal data level.

## Parameters

Image (input_object)  (multichannel-)image object (byte / uint2 / real)

Input image.

SigmaGrad (input_control)  number (real / integer)

Amount of smoothing used for the calculation of the gradient. If Smoothing is 'mean', SigmaGrad is ignored.

Default value: 1.0

Suggested values: 0.7, 0.8, 0.9, 1.0, 1.2, 1.5, 2.0, 3.0

Typical range of values: 0.7 ≤ SigmaGrad ≤ 50.0

Recommended increment: 0.1

SigmaInt (input_control)  number (real / integer)

Amount of smoothing used for the integration of the gradients.

Default value: 2.0

Suggested values: 0.7, 0.8, 0.9, 1.0, 1.2, 1.5, 2.0, 3.0

Typical range of values: 0.7 ≤ SigmaInt ≤ 50.0

Recommended increment: 0.1

Restriction: SigmaInt > 0.0

SigmaPoints (input_control)  number (real / integer)

Amount of smoothing used in the optimization functions.

Default value: 3.0

Suggested values: 0.7, 0.8, 0.9, 1.0, 1.2, 1.5, 2.0, 3.0

Typical range of values: 0.7 ≤ SigmaPoints ≤ 50.0

Recommended increment: 0.1

Restriction: SigmaPoints >= SigmaInt && SigmaPoints > 0.6

ThreshInhom (input_control)  number (real / integer)

Threshold for the segmentation of inhomogeneous image areas.

Default value: 200

Suggested values: 50, 100, 200, 500, 1000

Restriction: ThreshInhom >= 0.0

ThreshShape (input_control)  real (real)

Threshold for the segmentation of point areas.

Default value: 0.3

Suggested values: 0.1, 0.2, 0.3, 0.4, 0.5, 0.7

Typical range of values: 0.01 ≤ ThreshShape ≤ 1

Minimum increment: 0.01

Recommended increment: 0.1

Restriction: 0.0 <= ThreshShape && ThreshShape <= 1.0

Smoothing (input_control)  string (string)

Used smoothing method.

Default value: 'gauss'

List of values: 'gauss', 'mean'

EliminateDoublets (input_control)  string (string)

Elimination of multiply detected points.

Default value: 'false'

List of values: 'false', 'true'

RowJunctions (output_control)  point.y-array (real)

Row coordinates of the detected junction points.

ColumnJunctions (output_control)  point.x-array (real)

Column coordinates of the detected junction points.

CoRRJunctions (output_control)  number-array (real)

Row part of the covariance matrix of the detected junction points.

CoRCJunctions (output_control)  number-array (real)

Mixed part of the covariance matrix of the detected junction points.

CoCCJunctions (output_control)  number-array (real)

Column part of the covariance matrix of the detected junction points.

RowArea (output_control)  point.y-array (real)

Row coordinates of the detected area points.

ColumnArea (output_control)  point.x-array (real)

Column coordinates of the detected area points.

CoRRArea (output_control)  number-array (real)

Row part of the covariance matrix of the detected area points.

CoRCArea (output_control)  number-array (real)

Mixed part of the covariance matrix of the detected area points.

CoCCArea (output_control)  number-array (real)

Column part of the covariance matrix of the detected area points.

## Result

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 is raised.

## References

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.

## Module

Foundation

 Operators