Complex 2D Matched filter (CMF) based on the Matched filter approach was developed for palm vein extraction from noisy images. This filtering approach enables to carry out computations more efficiently, because of the one filtering mask. Filtering mask consists of  real and imaginary part, therefore it is called complex. The result of such filtering is a matrix of vectors, where in each input image pixel the vector is constructed. Vectors represent the similarity between image and filtering mask in certain region. This vector information is significant for further processing tasks.

Example of the CMF masks 

Example of palm vein image and filtering result with CMF