Laboratory Medicine in Psychiatry and Behavioral Sciences - Essay Example

This is in the sense of the concentrated light soft bounds at the center. Just as original Image A, Image C looks similar to Image C1 after the logarithmic transformation.
Exercise II
1 2 3

Above are images (1) original, (2) the transformed image of (1), and (3) the reverse transformation of image (2). The original image (1) demonstrates the Fourier transmutation. The reverse image is available to reconstruct the original image which is a replica in the pixels and luminance. The reconstruction of the original image can be done through inverse Fourier transformation as depicted in the image (3). The transformation of the original image (2) has a high frequency in the center image hence it is viewed as a dot. (Sandra A, 2012)

1A 2A 3A
Using the example above, the results of the prior exercise can be absolved through the images (1A), (2A), and (3A).
Exercise III
(i) (ii)

Image (i) is a circle image due to incoherent noise and its respective transformation image (ii). Image (i) indicates a random and even noise spread all over while image (ii) depicts a partial noise removal from the filtered image.

(iii) (iv)
Image (iii) is a circle with a coherent, regular noise in the vertical direction. The image also has a sharp edge. The transformed image (iv) indicates the inexistence of lines yet there appear wave-like circles around the dot to demonstrate the existence of soft noise. The wave-like circles disappear when we move to the outside of the dot. This indicates a lack of noise at the borders of the image. In comparison to the entire four images, (ii) appears sharper than (iv). Therefore, Fourier is able to separate the noise from the image in a regular noise but remove just a few in a random noise.

Exercise IV
1 2 3
In the figures above, (1) is an ideal lowpass filter, (2) is the original circle through a filtered spectrum with incoherent noise, and (3) is an inverse transformation of (2). The final image is made better than the original image through the application of a lowpass filter and the production of low frequency through the filtered spectrum of the original image. The final image shows more details and is brighter than the image (1). Hence the lowpass filter is vital for noise removal from the image for better visibility.

Exercise V
A1 A2 A3
In the figures above, A1 is the Butterworth filter, A2 is the filtered spectrum of the original circle image that has incoherent noise and A3 is the inverse transformation of A2. Image A1 has a middle-high frequency that decreases to the exterior of the image. Image A2 which is a filtered spectrum has a high frequency in the middle which results in a more detailed image. There is a decrease in the spectrum amplitude towards the nooks of the image. There is more detail with less noise in the final image A3in relation to the original image. This is a clear indication of the importance of the Butterworth filter in noise removal from the image. This makes the final image visible and more detailed.
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