condition can be obtained in an analogous fashion. Phase congruency-based A recent development in edge detection techniques takes a frequency domain approach to finding edge locations. Phase congruency (also known as phase coherence) methods attempt to find locations in an image where all sinusoids in the frequency domain are in phase. These locations will generally correspond to the location of a perceived edge, regardless of whether the edge is represented by a large change in intensity in the spatial domain. A key benefit of this technique is that it responds strongly to Mach bands, and avoids false positives typically found around roof edges. A roof edge, is a discontinuity in the first order derivative of a grey-level profile. Phase Stretch Transform (PST) The phase stretch transform or PST is a physics-inspired computational approach to signal and image processing. One of its utilities is for feature detection and classification. PST is a spin-off from research on the time stretch dispersive Fourier transform. PST transforms the image by emulating propagation through a diffractive medium with engineered 3D dispersive property (refractive index). The operation relies on symmetry of the dispersion profile and can be understood in terms of dispersive eigenfunctions or stretch modes. PST performs similar functionality as phase contrast microscopy but on digital images. PST is also applicable to digital images as well as temporal, time series, data. Subpixel To increase the precision of edge detection, several subpixel techniques had been proposed, including curve-fitting, moment-based, reconstructive, and partial area effect methods. These methods have different characteristics. Curve fitting methods are computationally simple but are easily affected by noise. Moment-based methods use an integral-based approach to reduce the effect of noise, but may require more computations in some cases. Reconstructive methods use horizontal gradients or vertical gradients to build a curve and find the peak of the curve as the sub-pixel edge. Partial area effect methods are based on the hypothesis that each pixel value depends on the area at both sides of the edge inside that pixel, producing accurate individual estimation for every edge pixel. Certain variants of the moment-based technique have been shown to be the most accurate for isolated edges. See also Edge-preserving filtering Feature detection (computer vision) for other low-level feature detectors Image derivative Gabor filter Image noise reduction Kirsch operator for edge detection in the compass directions Ridge detection for relations between edge detectors and ridge detectors Log