Interpolation

The difference between different interpolation methods will be observed by applying successive rotations on the image chess.png. The rotations will be made by using skimage.transform.rotate, which permits to choose different interpolation approaches.

• Perform four successive rotations of 90° of the image, and observe the effect of the rotation at each step. Use the default value for each parameter.

• Compare the resulting image with the original one, both visually and using the MSE.

• Now perform nine rotations of 40° and compare with the original image. What do you observe?

• Compare the previous result with other interpolation methods.

Correction

First, make rotations of angle 90° with a 0-order (nearest neighbour) interpolation.

Rotation with rotations of angle 90° and 0-order interpolation, MSE = 0.000:

In this configuration, the mean square error (MSE) is zero, meaning that the interpolations made along the sequence of rotation are perfect, i.e. the image is not changed.

Now, make rotations of angle 40°, with different interpolations (nearest neigbour, bilinear and bicubic).

Rotation with rotations of angle 40° and 0-order interpolation, MSE = 0.325:

Rotation with rotations of angle 40° and 1-order interpolation, MSE = 0.184:

Rotation with rotations of angle 40° and 3-order interpolation, MSE = 0.137:

In this example, a visual inspection of the result (last image) clearly shows that the nearest-neigbour interpolation is not satisfactory. This is confirmed by the MSE which is not the best MSE among the different results given by the interpolations.

In this example, the best interpolation is given by the bicubic interpolation.

Try to compare the results for different step angles, and different images!