Exercises on image filtering

We consider a matrix b(4,4) representing samples of an image B, such that:

Question

Filter this image using the 3x3 centered bidimensional rectangular filter of impulse response h(k,l):

Solution

We now consider a filter h(k,l) of impulse response:

Question

Write this impulse response as function of a sum of shifted delta function.

Solution

Question

Show that filter h(k,l) is separable. To do so, you will determine two monodimensional filters h1(k) et h2(l) verifying:

We now consider an image a(k,l):

Solution

Question

Calculate a**h and (a*h1)*(h2T). Conclusion?

Solution

Answer the following question.

Question

We consider a film of dynamic range D =3.6 (given in optical density units). What is the minimum number of bits that we must use to quantize the luminance of an image registered on this film so that the quantization error is invisible to a typical observer?

Solution

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