Non-down-sampled Contourlet (NSCT) transform

As the name implies, NSCT transformation Core is contourlet, that is, about the edge of the transformation.

The so-called non-bottom sampling is based on the frequency domain, according to the individual understanding, this is equivalent to a certain image, the first set a frequency threshold, and then filter out by the filter is greater than the threshold frequency of the image (of course, this is not a one-time screening process, but iterative use of a non-second channel bandpass filter process) See Figure 1 below for a detailed procedure.

At this point, if the airspace, frequency domain, time domain do not know, it is a group of paste. About these three concepts can refer to the " image processing and Recognition learning summary " " Digital Image processing 3--space domain, time domain, frequency domain understanding " two blog posts.

Again NSCT transformation, NSCT decomposition is conducive to better maintain image edge information and contour structure, enhance the image translation invariance. The process is divided into two processes of multi-scale decomposition and directional filtering, which are independent of each other.

The multi-scale decomposition of NSCT is a non-bottom-sampled tower decomposition ("tower shape", Laplace transform, wavelet transform, Contourlet transform are typical pyramid transformations), and its directional filtering adopts the non-lower sampling direction filter group (NSDFB).

In the process of decomposition and reconstruction of NSCT, there is no upper sampling and lower sampling process, which inherits the multi-directionality and anisotropy of traditional CT image representation, and has no translational invariance with traditional Ct. (not quite understood for "translational invariance")

The decomposition process of the non-bottom-sampled pyramid transform (NSP) has no sampling operation, and its reconstruction process is the inverse process of decomposition process.

The above can be referenced in the blog "image Fusion method based on NSCT and Fuzzy logic"

Non-down-sampled Contourlet (NSCT) transform