Invariant features for gray scale images

Self-learning Segmentation and Classification of Cell-Nuclei in 3D Volumetric Data Using Voxel-Wise Gray Scale Invariants

“…Gray scale features, invariant towards Euclidean motion, using Haar-integration over the whole transformation group of an n-dimensional data set X, are calculated as follows: [3] [5]…”

“…We introduce a new general purpose algorithm using voxelwise gray scale invariants( [1][2]) for both, segmentation and classification of cells in 2D and 3D probes, and provide some first, promising experimental results. Motivated by the work of [3] and [4], gray scale invariants were very successfully applied to individual pollen recognition in [5] [6]. A major problem of cell classification in tissue probes is segmentation.…”

General-purpose object recognition in 3D volume data sets using gray-scale invariants - classification of airborne pollen-grains recorded with a confocal laser scanning microscope

“…A quite simple but very powerful way of a general feature extraction is the computation of so-called "gray-scale invariants", which were described first for two-dimensional image data [11,3], but can be straightforwardly extended to three-dimensional volumetric data [10]. These gray-scale invariants do not need any segmentation within the object, but operate directly on the gray-values of the data set.…”

“…) feature space (n-dim.) The basic recipe for calculating these invariants is to take a non-linear kernel function of local support f (X) in order to relate or combine the grey scale values of some neighboring pixels or voxels and to integrate the result of this function over all possible representations of the object in the equivalence class [11].…”

“…In contrast to such approaches, we use 3D volume data and a general-purpose feature extraction, namely Euclidian gray-scale invariants [11,3], and we employ a classifier (a set of Support Vector Machines [13]) that is trained automatically with a labeled reference data base. In our programs the only a priori assumption is, that the objects are rigid and have random orientations and positions.…”