Problem $1(10$ pts$)$ Open ct$1.$dcm$.$ Read CT data and plot the image. Make sure that image raw values are converted to HU values by using RescaleSlope and RescaleIntercept information contained in CT header. When plotting the image, specify the colormap limits to $[500,500].$ Calculate the maximum and minimum intensity values of the image.

$[$Hint$]$ When CT data is loaded in MATLAB, it is read as unit$16(16-$bit unsigned integer type$).$ The data may need to be converted to int$16(16-$bit signed integer type$).$ In this case, please use int$16()$ function in MATLAB. This process is particularly relevant to the step of generating a normalized histogram using MATLAB function $$imhist$$ in Problem $2.$ But, you can process data using any methods that can appropriately generate a histogram.

e$.$g$.$ image$\_$raw $=$ int$16($image$\_$raw$)$;

Problem $2(15$ pts$)$ Crop the above image so that only the patient body is selected and the couch is removed $($you may create a new matrix that only contains the selected region$).$ To select a region, you will need to select a range of indices in the horizontal and vertical direction, respectively. Plot the cropped image and the corresponding normalized histogram. Keep in mind that if intensity values are appropriately represented as HU values, the values around $1000($air$)$ and $0($water$)$ should be prevalent in the histogram. Also, specify the colormap limits to $[500,500].$