Edge detection
It can be shown that under rather general assumptions for an image formation model, discontinuities in image brightness are likely to correspond to:[2][3] In the ideal case, the result of applying an edge detector to an image may lead to a set of connected curves that indicate the boundaries of objects, the boundaries of surface markings as well as curves that correspond to discontinuities in surface orientation.
If the edge detection step is successful, the subsequent task of interpreting the information contents in the original image may therefore be substantially simplified.
However, it is not always possible to obtain such ideal edges from real life images of moderate complexity.
In contrast a line (as can be extracted by a ridge detector) can be a small number of pixels of a different color on an otherwise unchanging background.
Similarly, if the intensity differences between the adjacent neighboring pixels were higher, one could argue that more than one edge should be considered to exist, or even none at all.
There are many methods for edge detection, but most of them can be grouped into two categories, search-based and zero-crossing based.
[7] John Canny considered the mathematical problem of deriving an optimal smoothing filter, given the criteria of detection, localization and minimizing multiple responses to a single edge.
[9] It took less than two decades to find a modern geometric variational meaning for that operator, that links it to the Marr–Hildreth (zero crossing of the Laplacian) edge detector.
[11] Edge detectors that perform better than the Canny usually require longer computation times or a greater number of parameters.
[14] The differential edge detector described below can be seen as a reformulation of Canny's method from the viewpoint of differential invariants computed from a scale space representation leading to a number of advantages in terms of both theoretical analysis and sub-pixel implementation.
In that aspect, Log Gabor filter have been shown to be a good choice to extract boundaries in natural scenes.
It is possible to extend filters dimension to avoid the issue of recognizing edge in low SNR image.
This method finds connected set of pixels having a directional derivative magnitude larger than a fairly small threshold.
Then, the distance transform operation is applied to the binary image to clear the pixels far from the background, so blob-like shapes or other false labeled regions are deleted from the edge map.
This removes all the unwanted points, and if applied carefully, results in one pixel thick edge elements.
Advantages: There are many popular algorithms used to do this, one such is described below: The number of passes across direction should be chosen according to the level of accuracy desired.
Thus, in the ideal continuous case, detection of zero-crossings in the second derivative captures local maxima in the gradient.
It can be shown, however, that this operator will also return false edges corresponding to local minima of the gradient magnitude.
A more refined second-order edge detection approach which automatically detects edges with sub-pixel accuracy, uses the following differential approach of detecting zero-crossings of the second-order directional derivative in the gradient direction: Following the differential geometric way of expressing the requirement of non-maximum suppression proposed by Lindeberg,[4][18] let us introduce at every image point a local coordinate system
has been computed, we can require that the gradient magnitude of the scale space representation, which is equal to the first-order directional derivative in the
according to: corresponding to the following filter masks: Higher-order derivatives for the third-order sign condition can be obtained in an analogous fashion.
A key benefit of this technique is that it responds strongly to Mach bands, and avoids false positives typically found around roof edges.
[19] The phase stretch transform or PST is a physics-inspired computational approach to signal and image processing.
PST transforms the image by emulating propagation through a diffractive medium with engineered 3D dispersive property (refractive index).
[22] 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.
To increase the precision of edge detection, several subpixel techniques had been proposed, including curve-fitting, moment-based,[23][24] reconstructive, and partial area effect methods.
Moment-based methods use an integral-based approach to reduce the effect of noise, but may require more computations in some cases.
This approach is particularly effective for detecting edges with clear boundaries in images while minimizing false positives due to noise, making it a valuable tool in computer vision applications where accurate edge localization is crucial.
Tazi, A. Jain and Deepika, "Edge Detection Using Modified Firefly Algorithm", Computational Intelligence and Communication Networks (CICN) 2014 International onference on, pp.
