Digital image is an array of small squares called pixels pic

Digital image is an array of small squares called pixels [picture elements]. The gray scale of an image is usually from 0= black to 256= white. So each pixel is assigned a number in the range 0 to 256. Histogram of an image describes the gray scale. On the x axis, we have {0,1,...,256] and on the y axis, we show their frequency. Each of the two given pictures has its Histogram next to it. Write what you can on the relation between an image and its histogram

Solution

Ans: The two images given here are the gray scale image i.e is contrast depends only on black & white.Now in cach portion there is a scale of depth of the grey as given, 0=black & 256=white.Now in the histogram along x-axis there is the grey scale & along y-axis there the no of counts that a given secale has.Basically for each pixel there is a correnponding grey scale value.And the total number of frequency (corresponding each grey scale value) is equal to the total no of pixel in the image.Taking this thing in mind we have,

in 1st image:We can see that the over all image is whitish i.e the grey scale value of each pixel is higher i.e towards the white(256) value.And this is shown in the histogram, we can see in the 1st histgram that the frequencys are high after the half of the grey scale (x-axis).And there is almost no dark black point in that image so the corresponding frequencies are zero.And the over all contrast of this image is bad.

Now in the 2nd image the contrast is very good as we can see that this 2nd image is more clear than that of the 1st image.In the 2nd image both the black points and the white point are present so this histogram is spreading all around i.e from the lower value of the grey scale(black region) to the higher value of the grey scale(white region).

Another approach: Basically the Blurring, smoothing etc of any image is done in the image Fourier domain or in the Frequency domain.Now Here the 1st image is a blurred image but the 2nd image is a normal image.A blurred image can be formed from the by applying a Low-Pass filter in the fourier domain.The low pass filter onlt allow the lower frequencies and blocks the high frequency componemts.And thid technique produce Blurred image like the first one.In the 2nd histogram we can see that the highfrequency comonents has the small grey scale value(starting from 0) then if a Low pass filter is applied then only the frequency with high grey scale value will be passed.And then we will get the 1st image from the 2nd one.