Phase congruency
Encyclopedia
Phase congruency is a measure of feature significance in computer images, a method of edge detection
that is particularly robust against changes in illumination and contrast.
. It has been noted that edgelike features have many of their frequency components in the same phase. The concept is similar to coherence
, except that it applies to functions of different wavelength.
For example, the Fourier decomposition of a square wave
consists of sine
functions, whose frequencies are odd multiples of the fundamental frequency. At the rising edges of the square wave, each sinusoidal component has a rising phase; the phases have maximal congruency at the edges. This corresponds to the human-perceived edges in an image where there are sharp changes between light and dark.
A notable example is an image feature consisting of a single line, such as the letter "l". Many edge-detection algorithms will pick up two adjacent edges: the transitions from white to black, and black to white. On the other hand, the phase congruency map has a single line. A simple Fourier analogy of this case is a triangle wave
. In each of its crests there is a congruency of crests from different sinusoidal functions.
are usually applied prior to the calculation.
Edge detection
Edge detection is a fundamental tool in image processing and computer vision, particularly in the areas of feature detection and feature extraction, which aim at identifying points in a digital image at which the image brightness changes sharply or, more formally, has discontinuities...
that is particularly robust against changes in illumination and contrast.
Foundations
Phase congruency reflects the behaviour of the image in the frequency domainFrequency domain
In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time....
. It has been noted that edgelike features have many of their frequency components in the same phase. The concept is similar to coherence
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....
, except that it applies to functions of different wavelength.
For example, the Fourier decomposition of a square wave
Square wave
A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels...
consists of sine
Sine
In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....
functions, whose frequencies are odd multiples of the fundamental frequency. At the rising edges of the square wave, each sinusoidal component has a rising phase; the phases have maximal congruency at the edges. This corresponds to the human-perceived edges in an image where there are sharp changes between light and dark.
Advantages
The square-wave example is naive in that most edge detection methods deal with it equally well. For example, the first derivative has a maximal magnitude at the edges. However, there are cases where the perceived edge does not have a sharp step or a large derivative. The method of phase congruency applies to many cases where other methods fail.A notable example is an image feature consisting of a single line, such as the letter "l". Many edge-detection algorithms will pick up two adjacent edges: the transitions from white to black, and black to white. On the other hand, the phase congruency map has a single line. A simple Fourier analogy of this case is a triangle wave
Triangle wave
A triangle wave is a non-sinusoidal waveform named for its triangular shape.Like a square wave, the triangle wave contains only odd harmonics...
. In each of its crests there is a congruency of crests from different sinusoidal functions.
Disadvantages
Calculating the phase congruency map of an image is very computationally intensive, and sensitive to image noise. Techniques of noise reductionNoise reduction
Noise reduction is the process of removing noise from a signal.All recording devices, both analogue or digital, have traits which make them susceptible to noise...
are usually applied prior to the calculation.
External links
- Research page of Peter Kovesi, list of research papers, example images and implementations.