Computer-Aided Intelligent Recognition Techniques and Applications 2005 John Wiley & Sons, Ltd

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Recognizing ROIs in Medical Images

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segmentation algorithms has been proposed in the literature [3]. There is a variety of such segmentation methods: histogram thresholding; edge following; tree/graph-based segmentation; region growing; clustering; probabilistic and Bayesian segmentation; neural network segmentation.

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One major problem present in most of the above segmentation techniques is that they do not perform well with medical images, as their gray levels of different objects are relatively similar. The other major problem is choosing a suitable approach for isolating different objects from the backgrounds. The combination of some of the above techniques may produce better segmentation results for some images, but nothing is guaranteed. In contrast to the heuristic nature of these methods, three primitive segmentation operations remain intrinsic and suggest a more algorithmic tack if they have been tuned and geared well for medical images. These three primitive operations are based on convolution, thresholding and mathematical morphology. Hybridizing such operations and adding more blocks to the integration will contribute to drawing the roadmap for segmenting medical images.

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2. Convolutional Primitive Segmentation

Convolution is a mathematical operation that is fundamental to many common image processing processes. Convolution provides a mechanism for edge detection through multiplying together two arrays of numbers to produce a third array of numbers of the same dimensionality. This can be used in image processing to implement operators whose output pixel values are simple linear combinations of certain input pixel values. In an image processing context, one of the input arrays is normally an image. The second array is usually much smaller, and is also two-dimensional, and is known as the kernel. Figure 15.1 shows an example image and a kernel that we will use to illustrate the convolution operation. The convolution is performed by sliding the kernel over the image, generally starting at the top left corner, so as to move the kernel through all the positions where the kernel fits entirely within the boundaries of the image. Each kernel position corresponds to a single output pixel, the value of which is calculated by multiplying together the kernel value and the underlying image pixel value for each

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Figure 15.1 The convolution process requires an image and a kernel.

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Convolutional Primitive Segmentation

j 3 3 Kernel i i c( )

o(i, j )

Input c I(i 1, j 1) I(i, j 1) I(i + 1, j 1) I(i 1, j ) I(i, j ) I(i + 1, j ) I(i 1, j + 1) I(i, j + 1) I(i + 1, j + 1)

Output o(i, j )

Figure 15.2 Illustrating the process of convolution. of the cells in the kernel, and then adding all these numbers together [4]. Figure 15.2 illustrates this operation. Using convolution, the value of the output pixel O22 can be calculated as follows: O22 = I11 K00 + I12 K01 + I13 K02 + I21 K10 + I22 K11 + I23 K12 + I32 K20 + I32 K21 + I33 K22 (15.1)

The convolution process is a highly researched issue and it is affected by many factors. There are many types of convolution operator used in the literature [5] which either use a single kernel or multiple kernels. There are many single kernels that are only used for special effects (e.g. horizontal line detection, smoothing). Figure 15.3 illustrates the effect of two single kernels upon an X-ray image using smoothing and high-pass kernels: 1 16 1 2 1 2 4 2 1 2 1 1 1 1 1 9 1 1 1 1

Smoothing

High-pass

Figure 15.3 Using a single convolution kernel for smoothing.

Recognizing ROIs in Medical Images

However, multiple kernels are applied on the image in multiple stages. In particular, there are some notable multiple kernel convolution operators that we list herewith. The Roberts Cross operator performs a simple, quick to compute, 2D spatial gradient measurement on an image. The operator consists of a pair of 2 2 convolution kernels. One kernel is the other rotated by 90 . Gx 1 0 0 1 Gy 0 1 1 0 G = Gx + Gy

These kernels are designed to respond maximally to edges running at 45 to the pixel grid, one kernel for each of the two perpendicular orientations. We can see that the result image is very dark when applying the Roberts Cross operator to a mammogram. The Laplacian is a 2D isotropic measure of the second spatial derivative of an image. The Laplacian of an image highlights regions of rapid intensity change and is therefore often used for edge detection. 1 1 1 1 8 1 1 1 1 1 4 1 4 20 4 1 4 1

The Sobel operator performs a 2D spatial gradient measurement on an image and so emphasizes regions of high spatial frequency that correspond to edges. Typically, it is used to find the approximate absolute gradient magnitude at each point in an input image. Sobel kernels are: 1 2 1 0 0 0 1 2 1 1 0 1 2 0 2 1 0 1

These kernels are designed to respond maximally to edges running vertically and horizontally relative to the pixel grid, one kernel for each of the two perpendicular orientations. The kernels can be applied separately to the input image, to produce separate measurements of the gradient component in each orientation (call these Gx and Gy ). These can then be combined together to find the absolute magnitude of the gradient at each point G = G2 G2 and the orientation of that gradient. An approximate x y magnitude can be computed using: G = Gx + Gy . Compass edge detection is an alternative approach to the differential gradient edge detection. When using compass edge detection, the image is convoluted with a set of (in general eight) convolution kernels, each of which is sensitive to edges in a different orientation. For each pixel, the local edge gradient magnitude is estimated with the maximum response of all eight kernels at this pixel location: G = max Gi i = 1 to n where Gi is the response of the kernel i at the particular pixel position and n is the number of convolution kernels. The local edge orientation is estimated with the orientation of the kernel that yields the maximum response. Various kernels can be used for this purpose, and best of all are the Prewitt and the Kirsch kernels. Two templates out of the set of eight are: 1 1 1 1 2 1 1 1 1 1 1 1 1 2 2 1 1 1

The Kirsch edge detector [6] is another compass kernel. The masks given by these templates try to model the kind of gray-level change seen near an edge having various orientations. There is a mask for each of eight compass directions. For instance, K0 implies a vertical edge (horizontal gradient) at the pixel corresponding at the center of the mask. To find the edge, I is convolved with the eight masks at each pixel position. The response is the maximum of the responses of any of the eight masks and the directions quantified into eight possibilities.