A geometrically distorted image is corrected and the pixel values are assigned using resampling techniques as shown in the figure. In this context, which of the following options is/are CORRECT?
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Bilinear interpolation uses a 2x2 pixel neighbourhood; cubic convolution uses a 4x4 pixel neighbourhood.
Bilinear interpolation technique assigns the output pixel value based on a distance-weighted average of DN values of four (2 x 2) nearest pixels
Cubic interpolation technique assigns the output pixel value based on a distance-weighted average of DN values of sixteen (4 x 4) nearest pixels
Bilinear interpolation technique assigns the output pixel value based on a distance-weighted average of DN values of nine (3 x 3) nearest pixels
Cubic interpolation technique assigns the output pixel value based on a distance-weighted average of DN values of nine (3 x 3) nearest pixels
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The Correct Option isA, B
Solution and Explanation
Step 1: Frame resampling as choosing how many neighbouring input pixels to average. After geometric correction, an output pixel location projected onto the original distorted image generally lies between input pixel centres. Different resampling algorithms differ in how many neighbouring input DNs they average and what weighting function they use. Step 2: Nail down the bilinear neighbourhood size. Bi-linear means linear interpolation performed in two directions (rows then columns), and linear interpolation needs 2 points on each axis, giving $2\times2=4$ points total, a distance-weighted average of exactly 4 surrounding pixels. This confirms option (A) and rules out option (C)'s claim of 9 pixels. Step 3: Nail down the cubic convolution neighbourhood size. Cubic convolution fits a cubic interpolating function, which needs 4 support points along each axis, giving $4\times4=16$ points total, a distance-weighted average of 16 surrounding pixels. This confirms option (B) and rules out option (D)'s claim of 9 pixels. Step 4: Cross-check against nearest-neighbour resampling for contrast. Nearest-neighbour resampling (not listed here) uses only 1 pixel with no distance weighting. The progression 1 to 4 to 16 pixels for nearest-neighbour, bilinear, and cubic convolution respectively is the standard textbook result, confirming 4 for bilinear and 16 for cubic, never 9 for either. Step 5: Final answer. Bilinear interpolation uses a 2x2 (4-pixel) neighbourhood and cubic convolution uses a 4x4 (16-pixel) neighbourhood.\[ \boxed{\text{Options (A) and (B)}} \]
