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Multiscale Linear Feature Detection
One of the approaches to linear feature extraction is to regard the image as a two-dimensional function z(x,y) of the spatial variables x and y; and extract lines from this function using differential geometry properties. Steger (1998) used Guassian kernels in his method. Steger proposed an approach to line detection that uses an explicit model for lines and line profile models of increasing sophistication. A scale-space analysis is carried out for each of the models. This analysis is used to derive an algorithm in which lines and their widths can be extracted with subpixel accuracy. The algorithm uses a modification of the differential geometric approaches to detect lines and their corresponding edges. Since Gaussian masks are used to estimate the derivatives of the image, the algorithm scales to lines of arbitrary widths while always yielding a single response. The Gaussian kernels are given by equations 1, 2 and 3.

For discrete signals, the convolution masks are given by:


For the proposed line detector, the parameters that are taken into consideration are the line width w and its contrast h. To convert thresholds on w and h into thresholds the operator can use, first a s should be chosen such that


Scale-Space Tracking
The Gaussian operator involves compromises, One has to make a judgement and compromise between losing line pixels and eliminating noise pixels without distorting the shape of lines. On the one hand, by using a large value of s, the noise is reduced but one loses genuine line pixels. On the other hand, using a small values of s, local information about lines is not lost but noise and other unnecessary details are enhanced. To overcome this problem, Bergholm (1987) introduced the concept of coarse to fine feature tracking known as edge focusing. He has applied this principle for edge detection.

The steps in the line tracking algorithm based on Bergholm's approach are as follows:

• Create an initial coarse level line image using the Gaussian operator with an initial value of s = so.
• Then choose a scale step S that is so small that line points with high probability do not move more than one pixel during the line focusing step.
• Now apply the edge detector with s = so- S at pixels where lines were detected for s = so and at pixels in their immediate neighborhood. This means that at a finer scale image, line detection is performed only at a thin region around the lines at the coarse scale image.
• The line points at previous level are discarded and only the finer scale line points are accepted.
• Subsequent line points are detected in the same way i.e., line detection is performed in the border region of the image with s = so- S using the new value of s = so- 2S. Nnote that the threshold is used only for s = so and not at the finer scales.
• Line focusing continues until Gaussian smoothing is quite weak (for example s = 0.6)< /li >

Some of the advantages of this technique are:

• If weak lines at finer levels of resolution belong to an line segment that exists at a coarse level, then gaps may be filled by the focusing procedure.
• Weak lines at finer levels of resolution not belonging to the coarse level line segments will normally be neglected using continuous coarse-to-fine tracking.

Watershed Transformation
A non-parametric method was first developed for contour extraction in grey images, which relied in defining the contours as watershed. (Beucher, 1992) This method has been considerably improved with the tools of mathematical morphology using watershed transformation. The non-parametric method of contour extraction using watershed transformation in the earlier stages lead to over-segmentation of images. Later a strategy called Marker Controlled Segmentation. In this approach, user defines object markers and background markers so as to differentiate between the two and later segment the image using the gradient image. The gradient image is often used in watershed transformation, as the main criterion of segmentation is image homogeneity. (Beucher 1992).

Watershed analysis is well recognized as being useful for image segmentation and has been made computationally practical thanks to a fast technique presented by Vincent and Soille (1991). Watershed analysis uses an image's gradient magnitude as input to subdivide the image into low-gradient catchment basins surrounded by high-gradient watershed lines. The catchment basins consist of locally homogeneous connected sets of pixels. The watershed lines are made up of connected pixels exhibiting local maxima in gradient magnitude; to achieve a final segmentation, these pixels are typically absorbed into adjacent catchment basins.