Question

HW 5.1 Learn the Gaussian Filter. Calculate the convolution kernel for the Gaussian filter (Show your calculations and important parameters), apply on the noisy phantom, display both original and filtered images. Calculate the SNR and CNR. HW 5.2 Gaussian filter and mean filters are smoothing filters. For example, consider the bluring effect of the mean filter. Original $\frac{1}{9}\begin{bmatrix}1 & 1 & 1\\1 & 1 & 1\\1 & 1 & 1\end{bmatrix}$ = Blur (with mean filter) You can use them also for image sharpening as a part of unsharp filter. You can create a filter by combining two filters: one multiplies the intensities of the image by 2, and the other subtracts the blured image as follows: Original $\begin{bmatrix}0 & 0 & 0\\0 & 2 & 0\\0 & 0 & 0\end{bmatrix} - \frac{1}{9}\begin{bmatrix}1 & 1 & 1\\1 & 1 & 1\\1 & 1 & 1\end{bmatrix}$ = Sharpening Apply the unsharp filter operation given above to the noisy phantom using the Gaussian filter (instead of mean filter) you derived in HW5.1 and display the sharpened result.

          HW 5.1 Learn the Gaussian Filter. Calculate the convolution kernel for the Gaussian filter (Show your
calculations and important parameters), apply on the noisy phantom, display both original and
filtered images. Calculate the SNR and CNR.
HW 5.2 Gaussian filter and mean filters are smoothing filters. For example, consider the bluring effect
of the mean filter.
Original
$\frac{1}{9}\begin{bmatrix}1 & 1 & 1\\1 & 1 & 1\\1 & 1 & 1\end{bmatrix}$ = Blur (with mean filter)
You can use them also for image sharpening as a part of unsharp filter. You can create a filter by
combining two filters: one multiplies the intensities of the image by 2, and the other subtracts the	blured image as follows:
Original
$\begin{bmatrix}0 & 0 & 0\\0 & 2 & 0\\0 & 0 & 0\end{bmatrix} - \frac{1}{9}\begin{bmatrix}1 & 1 & 1\\1 & 1 & 1\\1 & 1 & 1\end{bmatrix}$ = Sharpening
Apply the unsharp filter operation given above to the noisy phantom using the Gaussian filter
(instead of mean filter) you derived in HW5.1 and display the sharpened result.

HW 5.1 Learn the Gaussian Filter. Calculate the convolution kernel for the Gaussian filter (Show your
calculations and important parameters), apply on the noisy phantom, display both original and
filtered images. Calculate the SNR and CNR.
HW 5.2 Gaussian filter and mean filters are smoothing filters. For example, consider the bluring effect
of the mean filter.
Original
(1)/(9)
< b m a t r i x > = Blur (with mean filter)
You can use them also for image sharpening as a part of unsharp filter. You can create a filter by
combining two filters: one multiplies the intensities of the image by 2, and the other subtracts the blured image as follows:
Original
< b m a t r i x >
- (1)/(9)
< b m a t r i x > = Sharpening
Apply the unsharp filter operation given above to the noisy phantom using the Gaussian filter
(instead of mean filter) you derived in HW5.1 and display the sharpened result.

Added by Roger S.

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