Question

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?

• A. Bilinear interpolation technique assigns the output pixel value based on a distance-weighted average of DN values of four (2 x 2) nearest pixels
• B. Cubic interpolation technique assigns the output pixel value based on a distance-weighted average of DN values of sixteen (4 x 4) nearest pixels
• C. Bilinear interpolation technique assigns the output pixel value based on a distance-weighted average of DN values of nine (3 x 3) nearest pixels
• D. Cubic interpolation technique assigns the output pixel value based on a distance-weighted average of DN values of nine (3 x 3) nearest pixels

Hint:

Bilinear interpolation uses a 2x2 pixel neighbourhood; cubic convolution uses a 4x4 pixel neighbourhood.

Answer 1

The Correct Option is A, B

Step 1: Recall the standard resampling methods used in geometric correction.
When a distorted image is geometrically corrected, every output pixel location is mapped back onto the original distorted image, and this mapped location almost never falls exactly on an input pixel centre. A resampling rule computes the output DN from surrounding input pixels; the three standard methods are nearest neighbour (1 pixel), bilinear interpolation (4 pixels), and cubic convolution (16 pixels).
Step 2: Describe bilinear interpolation precisely.
Bilinear interpolation uses the 4 nearest input pixels surrounding the mapped point, arranged in a \(2\times2\) neighbourhood, and computes the output DN as a distance-weighted average of these 4 values by interpolating linearly first along one axis then the other. This matches option (A), and directly contradicts option (C), which wrongly claims 9 (3x3) pixels are used.
Step 3: Describe cubic convolution precisely.
Cubic convolution uses a larger neighbourhood of the 16 nearest input pixels, arranged in a \(4\times4\) block centred on the mapped point, applying a cubic weighting function based on distance. This matches option (B), and directly contradicts option (D), which wrongly claims only 9 (3x3) pixels are used.
Step 4: Tie back to the figure.
The figure shows the corrected (upright) output grid overlaid on the tilted, distorted input grid; each output cell centre, once located inside the distorted grid, is exactly the point around which the 2x2 or 4x4 neighbourhood of input pixels is taken for bilinear or cubic resampling respectively.
Step 5: Conclusion.
Bilinear interpolation correctly uses 4 (2x2) pixels and cubic convolution correctly uses 16 (4x4) pixels.\[ \boxed{\text{(A) and (B) are correct}} \]