Problem $1.$ Use the Gaussian smoothed image resulted from Problems $3$ or $4.$ Now, we are going to find a $$rough$$ edge that describes the patient surface in $2-$D space using MATLAB

$($a$)$ First, find an intensity value, above which most of pixels corresponding to the patient can be selected. And obtain a binary image using the intensity value obtained $(0$: background, $1$: patient$).$ Either the basic global thresholding method or the Otsu$$ method can be used to find an intensity value. Plot the resulting image after thresholding.

$($b$)$ Perform a morphological closing so that there is no hole $($background pixel$)$ inside the foreground in the image resulted in Problem $5($a$).$ Plot the resulting binary image.

$($c$)$ Perform a morphological erosion on the resulting image from Problem $5($b$).$ Plot the resulting binary image.

$($d$)$ Subtract the resulting image of $($c$)$ from the resulting image of $($b$)$ so that, in the final image, the foreground pixels describe the edge of the patient geometry. Plot the resulting binary image.

Problem $2(20$ pts$)$ The goal of this problem is to segment the patient lungs by applying thresholds. Generate a binary image whose intensity values are $1$ only in the lung regions. To solve this problem, you may use the results from Problem $1.$ Plot the resulting binary image of the segmented patient lungs using MATLAB