Morphological image analysis

Abstract

We describe a morphological image analysis method to characterize black-and-white images in terms of geometry and topology by means of the Minkowski functionals. We present an algorithm to calculate these functionals in two and three dimensions and apply the method to random point patterns on square and cubic lattices.

Integral-geometry morphological image analysis

“…We attach to every germ p G a hypercubic grain C G . In the bulk limit N, PRwith "xed, the averages of the morphological quantities of the ensemble of con"gurations of the hypercubic grains C G are still given by (47) but the explicit expressions for M J and m J , "0, 2 , d are di!erent from those in Euclidean space [75].…”

Computer-aided diagnosis for diagnostically challenging breast lesions in DCE-MRI based on image registration and integration of morphologic and dynamic characteristics

“…Another family of characteristics that capture morphologic attributes is generated by Minkowski functionals (MFs) [22]. MF can characterize geometrical and topological space concepts such as shape, convexity, and connectivity and represent a simple yet precise tool for the analysis of geometrical structures in tumors.…”

“…To calculate the MFs, one can use an iterative technique that checks every voxel and updates the values if the voxel belongs to the tumor. The efficient algorithm that we have used is presented in [22]. For the classification, it can also make sense to look at normed Minkowski functionals, which arẽ…”

Characterizing neuromorphologic alterations with additive shape functionals

“…A recently reported [19,20] procedure for calculating additive shape functionals, known as Minkowski functionals gathered in a framework called IntegralGeometry Morphological Image Analysis, MIA, has been successfully applied to many areas of research including Statistical Physics, Cosmology and Material Sciences [21,22,19,20,23]. A first attempt to bring those morphological concepts into biological sciences, targeting the efficient discrimination of two main types of the domestic cat's ganglionary neuronal cells, has been reported recently [24].…”

“…This completeness extends to higher dimensions and the geometrical functionals multiplicity is always one plus the dimension of the lattice generalized voxels (e.g 3 in 2D plane, 4 in 3D space, etc.). While the theory of Integral geometry provides a sophisticated set of results and formulae, the practical implementation of the procedures in Image analysis is relatively simple and efficient [19,20]. The basic ideas of this methodology is described in section 2 and a simple example is worked out to outline the procedure.…”