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—We present the construction of combined blur and rotation moment invariants in arbitrary number of dimensions. Moment invariants to convolution with an arbitrary centrosymmetric filter are derived first, and then their rotationally invariant forms are found by means of group representation theory to achieve the desired combined invariance. Several examples(More)
In this paper we introduce a new theory of blur invariants. Blur invariants are image features which preserve their values if the image is convolved by a point-spread function (PSF) of a certain class. We present the invariants to convolution with an arbitrary N-fold symmetric PSF, both in Fourier and image domain. We introduce a notion of a primordial(More)
Processing of multidimensional image data which were acquired by a linear imaging system of unknown point-spread function (PSF) is an important problem whose solution usually requires image restoration based on blind deconvolution (BD). Since BD is an ill-posed and often impossible task, we propose an alternative approach that enables to skip the(More)
Moment invariants are features calculated on an image, which do not change their values after a transformation of the image. This paper focuses on the so called combined invariants, which obey additional requirement of in-variance to image blurring. Our first contribution is a review of achievements most relevant to the derivation of algebraic, moment and(More)
When a patient is examined by positron emission tomography (PET), radiotracer dose amount (activity) has to be determined. However, the rules for activity correction according to patients' weight used nowadays do not correspond with practical experience. Very high image quality is achieved for slim patients, whereas noisy images are produced for obese(More)
Functional properties of living tissues appear in PET, whereas structural information at significantly higher resolution and better image quality is provided by other modalities, such as CT or MRI. We illustrate how structural information of matched anatomic images can be used as priors in the total variation denoising and blind deconvolution of functional(More)
In this paper, we propose a novel approach to patch matching in exemplar-based inpainting. Our field of concern is movie restoration, particularly scratch concealment. Here we want to focus on a single frame (still image) inpainting. Exemplar-based approach uses patches from the known areas and copies their content to the damaged area. In case of irregular(More)
This work presents new application of the random field theory in medical imaging. Results from both integral geometry and random field theory can be used to detect locations with significantly increased radiotracer uptake in images from positron emission tomography (PET). The assumptions needed to use these results are verified on a set of real and(More)
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