35 research outputs found
Amoeba Techniques for Shape and Texture Analysis
Morphological amoebas are image-adaptive structuring elements for
morphological and other local image filters introduced by Lerallut et al. Their
construction is based on combining spatial distance with contrast information
into an image-dependent metric. Amoeba filters show interesting parallels to
image filtering methods based on partial differential equations (PDEs), which
can be confirmed by asymptotic equivalence results. In computing amoebas, graph
structures are generated that hold information about local image texture. This
paper reviews and summarises the work of the author and his coauthors on
morphological amoebas, particularly their relations to PDE filters and texture
analysis. It presents some extensions and points out directions for future
investigation on the subject.Comment: 38 pages, 19 figures v2: minor corrections and rephrasing, Section 5
(pre-smoothing) extende
Mathematical morphology on tensor data using the Loewner ordering
The notions of maximum and minimum are the key to the powerful tools of greyscale morphology. Unfortunately these notions do not carry over directly to tensor-valued data. Based upon the Loewner ordering for symmetric matrices this paper extends the maximum and minimum operation to the tensor-valued setting. This provides the ground to establish matrix-valued analogues of the basic morphological operations ranging from erosion/dilation to top hats. In contrast to former attempts to develop a morphological machinery for matrices, the novel definitions of maximal/minimal matrices depend continuously on the input data, a property crucial for the construction of morphological derivatives such as the Beucher gradient or a morphological Laplacian. These definitions are rotationally invariant and preserve positive semidefiniteness of matrix fields as they are encountered in DT-MRI data. The morphological operations resulting from a component-wise maximum/minimum of the matrix channels disregarding their strong correlation fail to be rotational invariant. Experiments on DT-MRI images as well as on indefinite matrix data illustrate the properties and performance of our morphological operators
Locally Adaptive Frames in the Roto-Translation Group and Their Applications in Medical Imaging
Left-Invariant Diffusions on the Space of Positions and Orientations and their Application to Crossing-Preserving Smoothing of HARDI images
Computer-aided diagnosis for diagnostically challenging breast lesions in DCE-MRI based on image registration and integration of morphologic and dynamic characteristics.
Diagnostically challenging lesions comprise both foci (small lesions) and non-mass-like enhancing lesions and pose a challenge to current computer-aided diagnosis systems. Motion-based artifacts lead in dynamic contrast-enhanced breast magnetic resonance to diagnostic misinterpretation; therefore, motion compensation represents an important prerequisite to automatic lesion detection and diagnosis. In addition, the extraction of pertinent kinetic and morphologic features as lesion descriptors is an equally important task. In the present paper, we evaluate the performance of a computer-aided diagnosis system consisting of motion correction, lesion segmentation, and feature extraction and classification. We develop a new feature extractor, the radial Krawtchouk moment, which guarantees rotation invariance. Many novel feature extraction techniques are proposed and tested in conjunction with lesion detection. Our simulation results have shown that motion compensation combined with Minkowski functionals and Bayesian classifier can improve lesion detection and classification
PDE-based Morphology for Matrix Fields: Numerical Solution Schemes
Tensor fields are important in digital imaging and computer vision. Hence there is a demand for morphological operations to perform e.g. shape analysis, segmentation or enhancement procedures. Recently, fundamental morphological concepts have been transferred to the setting of fields of symmetric positive definite matrices, which are symmetric rank two tensors. This has been achieved by a matrixvalued extension of the nonlinear morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images. Having these two basic operations at our disposal, more advanced morphological operators such as top hats or morphological derivatives for matrix fields with symmetric, positive semidefinite matrices can be constructed. The approach realises a proper coupling of the matrix channels rather than treating them independently. However, from the algorithmic side the usual scalar morphological PDEs are transport equations that require special upwind-schemes or nove