Invariant Measures of Image Features From Phase Information

Peter Kovesi

If reliable and general computer vision techniques are to be developed it is crucial that we find ways of characterizing low-level image features with invariant quantities. For example, if edge significance could be measured in a way that was invariant to image illumination and contrast, higher-level image processing operations could be conducted with much greater confidence. However, despite their importance, little attention has been paid to the need for invariant quantities in low-level vision for tasks such as feature detection or feature matching.

In my research I have developed a number of invariant low-level image measures for feature detection, local symmetry/asymmetry detection, and for signal matching. These invariant quantities are developed from representations of the image in the frequency domain . In particular, phase data is used as the fundamental building block for constructing these measures. Phase congruency can be used as an illumination and contrast invariant measure of feature significance. This allows edges, lines and other features to be detected reliably, and fixed thresholds can be applied over wide classes of images. Points of local symmetry and asymmetry in images can be detected from the special arrangements of phase that arise at these points, and the level of symmetry/asymmetry can be characterized by invariant measures. It is also possible to perform signal matching using correlation of local phase and amplitude information. This approach allows reliable phase based disparity measurements to be made, overcoming many of the difficulties associated with scale-space singularities.

Relevant Papers:

Thesis:

Technical Report:

MATLAB Code For Calculating Phase Congruency:

phasecong.m MATLAB code for calculating Phase Congruency and Phase Symmetry/Asymmetry.

nonmaxsup.m MATLAB code for non-maxima suppression.

hysthresh.m MATLAB code for hysteresis thresholding.

Example MATLAB session: 


 >> im = imread('picci.tif');             % Read the image 
 >> image(im);                            % Display the image
 >> [pc orient ft] = phasecong(im);       % Calculate phase congruency.
 >> imagesc(pc);                          % Display the phase congruency image
 >> nonmax = nonmaxsup(pc, orient, 1.5);  % Perform non-maximal suppression
 >> features =  hysthresh(nonmax, 0.3, 0.15); % Hysteresis threshold
 >> imagesc(features);                    % Look at the result

Some Results

Mandrill image

Raw phase congruency image obtained from phasecong.m. Phase congruency is a dimensionless quantity, its value ranges between 0 and 1. Step and line features are marked equally well. Note how each whisker has been marked as a single feature.

Phase Congruency edge map obtained after non-maxiam suppression (using nonmaxsup.m) and hysteresis thresholding between phase congruency values of 0.3 and 0.15 (using hysthresh.m).

For comparison here is the raw Canny edge strength image (sigma = 1). Note how edges are marked on each side of each whisker.

Venice image

Raw phase congruency image. Notice the response of the detector in the low contrast regions. Compare this to the output of the Canny detector below.

Phase congruency edge map obtained with non-maxima suppression and hysteresis thresholding between phase congruency values of 0.3 and 0.15.

Raw Canny edge strength image (sigma = 1). Note how the response of the Canny detector collapses in the low contrast regions.

Whale image

Raw phase symmetry image (obtained using phasecong.m). Phase symmetry is a dimensionless quantity, its value ranges between 0 and 1. It detects symmetry of features independent of contrast.

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