Mathematical morphology Essay

In signal processing, it is often desirable to be able to perform some kind of noise reduction on an image or signal. The median filter is a nonlinear digital filtering technique, often used to remove noise. Such noise reduction is a typical preprocessing step to improve the results of later processing (for example, edge detection on an image).

C. Dilation

Dilation is the dual of erosion. At each translated location, the structuring element values are subtracted from the image pixel values and the minimum is computed. The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels (i.e. white pixels, typically). Thus areas of foreground pixels grow in size while holes within those regions become smaller. The dilation operator takes two pieces of data as inputs. The first is the image which is to be dilated.

D. Edge detection

The Sobel operator is used in image processing, particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of the image intensity function. At each point in the image, the result of the Sobel operator is either the corresponding gradient vector or the norm of this vector. The Sobel operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical direction and is therefore relatively inexpensive in terms of computations.

Filtering

By using median filter, we filter the image for removing the noise from the figure and make it suitable for further processing.

DWT algorithm

After applying DWT algorithm, we segment our input biomedical image and find the average component and after we found our region of interest we use in parameter calculations.

Parameter Calculations

After applying DWT algorithm, we calculate the parameter of the image like standard deviation, entropy, texture which is different for each type of image. And those values will be used further for disease diagnosis.

Standard parameter

In this operation, we compare our input image parameter with the standard image parameter of lungs and when mismatch is found which means there is defect in our lung image i.e. disease is diagnosed and for the reverse vice versa.

Wavelet transform is used to convert a spatial domain into frequency domain. The use of wavelet in an image stenographic model lies in the fact that the wavelet transform clearly separates the high frequency and low frequency information on a pixel by pixel basis. Discrete Wavelet Transform (DWT) is preferred over Discrete Cosine Transforms (DCT) because image in low frequency at various levels can offer corresponding resolution which is needed. A one dimensional DWT is a repeated filter bank algorithm, and the input is convolved with high pass filter and a low pass filter. The result of latter convolution is smoothed version of the input, while the high frequency part is captured by the first convolution. The reconstruction involves a convolution with the synthesis filter and the results of this convolution are added.