In digital image processing, geometric conversion from the two basic operations: (1) the coordinate transformation; (2) the interpolated grayscale
Define (v, w) are the coordinates of the original image, (x, Y) is the image coordinates after conversion, there are (x, y) = T (v, w), T represents a (v, w) to (x, y) after transformation. We usually call this transformation is the forward mapping, obtain coordinates of a transformation of coordinates before a conversion.
For the first term mapping, we may not be able to get the coordinates of all the image transformation.
If so S (x, y) = (v, w), S is the inverse matrix T, and we will each transformed coordinates in calculation, to find a corresponding coordinate before conversion, we call this converted reverse mapping.
After finding the positions corresponding to the original image, gray-scale values corresponding to assign points. Since the point found may not find exactly the corresponding point in the original image, this time we can use the nearest neighbor interpolation, bilinear interpolation, bicubic interpolation and other methods to calculate
Gradation value after conversion.
The nearest neighbor interpolation , the original image nearest neighbor grayscale value paid for each new position, is simple, but the converted image defects, such as severe distortion of the straight edge, is not used in practical use.
Bilinear interpolation, with the four nearest neighbor points to estimate the position of a given gradation. We let v (x, y) represents the gray scale value for the bilinear interpolation, the assignment is obtained by the following equation: v (x, y) = ax + by + cxy + d
We can see that, although the method name with "linear" word, which is not essentially an in linear interpolation.
Bicubic interpolation , which uses the 16 nearest neighbor assignment formula is as follows:
16 determination formulas is by a factor 16 may be adjacent to the closest point (x, y) of the point written unknown equations. If the lower limit of the summation formula are 0 and 1, the interpolation is bilinear. Bi-cubic interpolation is standard method commercial image editing program.
The code is implemented by the following two methods bilinear interpolation and bicubic.
Recently neighbor interpolation method