Fast algorithms in nD image analysis

Template library for multidimensional image processing and analysis

Multidimensional images templates and objects implemented with several separable algorithms for image processing and painting in C++. Several 2D and 3D usefull algorithms for processing and measurement are included.
Source code.

Sections of nD image

Orthogonal sections of n-dimensional image with dimensions 1 or n-1 can be calculated by simple algorithms using one programming cycle only. n-1-dimensional slicing of the array is used for visualization or analysis purposes. By iterating the slicing operation we can obtain section of arbitrary dimension. Traversing of rows and slices is used in separable algorithms like FFT, the Gaussian filter, Daubeschies wavelet filter or the squared Euclidean distance transform applying 1-dimensional operations on all rows successively in all directions.

Fast Fourier transform of real arrays

An inplace implementation of the real-valued n-dimensional FFT, based on ffteasy by G. Felder. The algorithm wraps the real array to complex array and then applies separable direct complex FFT for a direct operation, or calculates separable inverse complex FFT and unwraps the complex array to real array for inverse operation. The procedure for calculation of FT of convolution or correlation of two images are included as well as the procedure for calculation of FT of image with origin shifted to the centre of the image.
Source code.

Other separable nD transforms

Separable implementations of Gaussian filter, using either 1D convolution or fast recursive 1D algorithm (Young & van Vliet, 2002, Triggs & Sdika, 2006), of wavelet transform (Daubeschies, 1988), or of squared Euclidean distance transform (Breu et al., 1995). Gaussian description.

Recursive IA filters

There are several recursive implementation of image analysis filters with performance independent on filter kernel size, that can be easilly generalized to arbitrary dimension: erosion and dilation (van Herk, 1992), moving average (Glasbey and Jones, 1998) and median (Perreault and Hebert, 2009).

Lipschitz filter

The well known two-pass chamfer distance algorithm in nD (Borgefors, 1984) applied to grayscale images (Štencel & Janáček, 2006). ImageJ PlugIn

Graph cut regularization, segmentation or correspondence

Graph cut optimization enables updating the subsets of image elements or geometrical primitives simultaneously, which helps us solving various problems of image analysis and geometrical modelling.

Jiří Janáček