Intuitively, one should expect that how close together the samples are

should be a function of the spatial frequency in an image.

If the image intensity varies a lot and rapidly, which

means that there's a lot of high-frequency energy Then, intuitively,

one should use samples that are close together, so that

all of these first variations of intensity have captured the property.

If on the other hand, they have another flat image, then a few

samples will suffice, and this is exactly what the Nyquist theorem tells us.

So here is again the support of the spectrum of the analog image,

and lets call Omega n1 the highest frequency in the horizontal

direction and Omega n2 the highest frequency in the vertical direction.

After I sample this image, the spectrum of the

discrete image is desirable but it looks like this.

So in other words, there is no aliasing.

So this point is two pi over t1 and therefore the

point in here is two pi t1 minus Omega and one.

So clearly, as long as the ordering of these two points is as shown here.

So, as long as two pi over T1 minus omega n1 is greater or equal than

omega and one, there's no aliasing in the horizontal direction.

And this gives us the condition that the something frequency should be

at least twice as high as the highest frequency in the image.

And they can obtain the similar condition in the vertical direction, so the

something frequency in the vertical direction should

be greater equal then omega and two.

So if these two conditions are satisfied, then I can recover the analog image

from the discrete one by using a low pass filter, as shown here.