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A cornerstone of computational solid mechanics in the context of digital transformation are databases for microstructures obtained from advanced tomography techniques. Uniform discretizations of pixelized images in 2D are the raw-data point…
Digital images from crystals, as projected from the third spatial dimension and recorded in atomic resolution with any kind of real-world microscope, feature necessarily broken symmetries of the translation-periodicity-restricted Euclidean…
Image forensics, aiming to ensure the authenticity of the image, has made great progress in dealing with common image manipulation such as copy-move, splicing, and inpainting in the past decades. However, only a few researchers pay…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear…
This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We…
With the recent advancements in the field of information industry, critical data in the form of digital images is best understood by the human brain. Therefore, digital images play a significant part and backbone role in many areas such as…
Image denoising is an important pre-processing step in medical image analysis. Different algorithms have been proposed in past three decades with varying denoising performances. More recently, having outperformed all conventional methods,…
We report on a particular example of noise and data representation interacting to introduce systematic error. Many instruments collect integer digitized values and appy nonlinear coding, in particular square-root coding, to compress the…
In this paper, we evaluate dimensionality reduction methods in terms of difficulty in estimating visual information on original images from dimensionally reduced ones. Recently, dimensionality reduction has been receiving attention as the…
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…
Approximation theory plays an important role in image processing, especially image deconvolution and decomposition. For piecewise smooth images, there are many methods that have been developed over the past thirty years. The goal of this…
The traditional methods of image assessment, such as mean squared error (MSE), signal-to-noise ratio (SNR), and Peak signal-to-noise ratio (PSNR), are all based on the absolute error of images. Pearson's inner-product correlation…
Digital image correlation (DIC) is a well-established, non-invasive technique for tracking and quantifying the deformation of mechanical samples under strain. While it provides an obvious way to observe incremental and aggregate…
Modern digital cameras rely on the sequential execution of separate image processing steps to produce realistic images. The first two steps are usually related to denoising and demosaicking where the former aims to reduce noise from the…
Compression plays a significant role in a data storage and a transmission. If we speak about a generall data compression, it has to be a lossless one. It means, we are able to recover the original data 1:1 from the compressed file.…
Image compression is one of the essential methods of image processing. Its most prominent advantage is the significant reduction of image size allowing for more efficient storage and transfer. However, lossy compression is associated with…
Image quantization is used in several applications aiming in reducing the number of available colors in an image and therefore its size. De-quantization is the task of reversing the quantization effect and recovering the original…
Dual-energy computed tomography (DECT) has shown great potential and promising applications in advanced imaging fields for its capabilities of material decomposition. However, image reconstructions and decompositions under sparse views…
The problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences. In such cases, the degradation is typically caused by the…