For all the images below, a box filter of length 1 was used.

The following sampling methods were used:-

• Random
• Regular
• Jittering
• Multi-dimensional jittering
• An adaptive method described below.

          The circles indicate the sampling points

The value at the sampling points is compared to the average of the five points. If  the value at a sampling point differs by more than a threshold value from the average,  a recursive call is made on the square of lenght N/2 (if N is the length of the original square) surrounding that point. A limit is placed on the depth of the corresponding recursive tree.

Here is the result of the different sampling sizes and techniques on the first image
 

Number of samples ->	4	16	256
Random Sampling
Regular sampling
Jittered Sampling
Multi - jittered sampling
Adaptive Sampling	Threshold = 0.01		Maximum recursion depth = 12

 
 A Chess board as viewed from (1,0,0) looking at the point (1,1,0)
 

Number of samples ->	4	16	256
Random Sampling
Regular Sampling
Jittered Sampling
Multi-Jittered Sampling
Adaptive Sampling	threshold = 0.1		maximum recursion depth = 10

 
 
This was obtaining by using jittering 16 samples per pixel and using a tent filter.  There is something wrong since the white appears grayish.