Novel Entropy for Enhanced Thermal Imaging and Uncertainty Quantification.

This paper addresses the critical need for precise thermal modeling in electronics, where temperature significantly impacts system reliability. We emphasize the necessity of accurate temperature measurement and uncertainty quantification in thermal imaging, a vital tool across multiple industries. Current mathematical models and uncertainty measures, such as Rényi and Shannon entropies, are inadequate for the detailed informational content required in thermal images. Our work introduces a novel entropy that effectively captures the informational content of thermal images by combining local and global data, surpassing existing metrics. Validated by rigorous experimentation, this method enhances thermal images' reliability and information preservation. We also present two enhancement frameworks that integrate an optimized genetic algorithm and image fusion techniques, improving image quality by reducing artifacts and enhancing contrast. These advancements offer significant contributions to thermal imaging and uncertainty quantification, with broad applications in various sectors.

Image reconstruction from finite number of projections: method of transferring geometry.

This paper introduces a novel method of image reconstruction from a finite number of projections by processing the image along parallel rays. The geometry from the image plane is transferred to the Cartesian lattice by means of using the original image's line-integrals to calculate the line-sums of the discrete image to be reconstructed. Such a transformation of geometry allows for the 2D discrete paired transform, whose complete set of functions is defined by directions, to be effectively used in the exact reconstruction of the original image. The model of image reconstruction is described, and both examples and experimental results of implementation of the proposed method are provided for reconstruction on the Cartesian lattice of size 2(r) × 2(r), where r ≥ 2.

Principle of superposition by direction images.

This paper discusses the decomposition of the image by direction images, which is based on the concept of the tensor representation and its advanced form, the paired representation. The 2-D image is considered of the size N×N, where N is prime, a power of two, and a power of odd primes. The tensor and paired representations in the frequency-and-time domain define the image as a set of 1-D signals, which we call splitting-signals. Each of such splitting-signals is calculated as the sum of the image along the parallel lines, and it defines the direction image as a component of the original image. The unique decomposition of the image by direction images is described, and formulas for the inverse tensor and paired transforms are given. These formulas can be used for image reconstruction from projections, when splitting-signals or their direction images are calculated directly from the projection data. The number of required projections is uniquely defined by the tensor representation of the image.

Fast splitting alpha-rooting method of image enhancement: tensor representation.

In the tensor representation, a two-dimensional (2-D) image is represented uniquely by a set of one-dimensional (1-D) signals, so-called splitting-signals, that carry the spectral information of the image at frequency-points of specific sets that cover the whole domain of frequencies. The image enhancement is thus reduced to processing splitting-signals and such process requires a modification of only a few spectral components of the image, for each signal. For instance, the alpha-rooting method of image enhancement can be fulfilled through processing separately a maximum of 3N/2 splitting-signals of an image (N x N), where N is a power of two. In this paper, we propose a fast implementation of the a-rooting method by using one splitting-signal of the tensor representation with respect to the discrete Fourier transform (DFT). The implementation is described in the frequency and spatial domains. As a result, the proposed algorithms for image enhancement use two 1-D N-point DFTs instead of two 2-D N x N-point DFTs in the traditional method of alpha-rooting.

Method of paired transforms for reconstruction of images from projections: discrete model.

In this paper, an effective method of discrete image reconstruction from its projections is introduced. The method is based on the vector and paired representations of the two-dimensional (2D) image with respect to the 2D discrete Fourier transform. Such representations yield algorithms for image reconstruction by a minimal number of attenuation measurements in certain projections. The proposed algorithms are described in detail for an N x N image, when N = 2(r), r > 1. The inverse formulas for image reconstruction are given. The efficiency of the algorithms is expressed in the fact that they require a minimal number of multiplications, or can be implemented without such at all. The problem of discrete image reconstruction is also considered in three-dimensional (3D) space, namely on the 3D torus, where the reconstruction is performed by means of the nonlinear projections that are integral over 3D spirals on the torus.

Morphological spot counting from stacked images for automated analysis of gene copy numbers by fluorescence in situ hybridization.

Fluorescence in situ hybridization (FISH) is a molecular diagnostic technique in which a fluorescent labeled probe hybridizes to a target nucleotide sequence of deoxyribose nucleic acid. Upon excitation, each chromosome containing the target sequence produces a fluorescent signal (spot). Because fluorescent spot counting is tedious and often subjective, automated digital algorithms to count spots are desirable. New technology provides a stack of images on multiple focal planes throughout a tissue sample. Multiple-focal-plane imaging helps overcome the biases and imprecision inherent in single-focal-plane methods. This paper proposes an algorithm for global spot counting in stacked three-dimensional slice FISH images without the necessity of nuclei segmentation. It is designed to work in complex backgrounds, when there are agglomerated nuclei, and in the presence of illumination gradients. It is based on the morphological top-hat transform, which locates intensity spikes on irregular backgrounds. After finding signals in the slice images, the algorithm groups these together to form three-dimensional spots. Filters are employed to separate legitimate spots from fluorescent noise. The algorithm is set in a comprehensive toolbox that provides visualization and analytic facilities. It includes simulation software that allows examination of algorithm performance for various image and algorithm parameter settings, including signal size, signal density, and the number of slices.