We present a smooth geometric approach to discrete tomography that jointly performs tomographic reconstruction and label assignment. The flow evolves on a submanifold equipped with a Hessian Riemannian metric and properly takes into account given projection constraints. The metric naturally extends the Fisher-Rao metric from labeling problems with directly observed data to the inverse problem o...

In discrete tomography, a scanned object is assumed to consist of only a few different materials. This prior knowledge can be effectively exploited by a specialized discrete reconstruction algorithm such as the Discrete Algebraic Reconstruction Technique (DART), which is capable of providing more accurate reconstructions from limited data compared to conventional reconstruction algorithms. Howe...

Accurate segmentation of nanoparticles within various matrix materials is a difficult problem in electron tomography. Due to artifacts related to image series acquisition and reconstruction, global thresholding of reconstructions computed by established algorithms, such as weighted backprojection or SIRT, may result in unreliable and subjective segmentations. In this paper, we introduce the Par...

Enhancement of degraded images of binary shapes is an important task in many image processing applications, e.g. to provide appropriate image quality for optical character recognition. Although many image restoration methods can be found in the literature, most of them are developed for grayscale images. In this paper we propose a novel binary image restoration algorithm. As a first step, it re...

We propose a new algorithm for multivalued discrete tomography, that reconstructs images from few projections by approximating the minimum of a suitably constructed energy function with a deterministic optimization method. We also compare the proposed algorithm to other reconstruction techniques on software phantom images, in order to prove its applicability.

A convex programming approach to discrete tomographic image reconstruction in noisy environments is proposed. Conventional constraints are mixed with noise-based constraints on the sinogram and a binarity-promoting total variation constraint. The noise-based constraints are modeled as confidence regions that are constructed under a Poisson noise assumption. A convex objective is then minimized ...

A practical motivation of our inverse problem from discrete tomography comes from quality control in VLSI design. It demands a homogeneous crystaline layers consisting, e.g., of silicon. Homogenity “means non-roughness” of a considered atom cluster which is discrete and three dimensional. Scientists such as Gardner and Gritzmann ([5]) are interested in carrying over mathematical methods from hi...

In this paper, we present an iterative reconstruction algorithm for discrete tomography, 4 called DART (Discrete Algebraic Reconstruction Technique). DART can be applied if the scanned 5 object is known to consist of only a few different compositions, each corresponding to a constant 6 grey value in the reconstruction. Prior knowledge of the grey values for each of the compositions is 7 exploit...

Emission computed tomography with technetium-99m pyrophosphate was used to delineate the location and estimate the size of myocardial infarcts in 20 patients with documented acute myocardial infarction. Tomography was performed after planar imaging within 2-5 days after the onset of infarction. A series of transaxial, frontal, and sagittal tomograms were reconstructed from 32 views imaged from ...

Image fusion combines information from multiple images of the same scene to get a composite image that is more suitable for human visual perception or further image-processing tasks. In this paper the multi source medical images like MRI (Magnetic Resonance Imaging), CT (computed tomography) & PET (positron emission tomography) are fused using different multi scale transforms. We compare variou...