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 of the invariants are calculated explicitly to illustrate the proposed procedure. Their invariance, robustness, and capability of using in template matching and in image registration are demonstrated on 3D MRI data and 2D indoor images.

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 image as a canonical form of all blur-equivalent images. It is defined in spectral domain by means of projection operators. We prove that the moments of the primordial image are invariant to blur and we derive recursive formulae for their direct computation without actually constructing the primordial image. We further prove they form a complete set of invariants and show how to extent their invariance also to translation, rotation and scaling. We illustrate by simulated and real-data experiments their invariance and recognition power. Potential applications of this method are wherever one wants to recognize objects on blurred images.

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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 PET images. Experiments on phantom images and clinical data validate the proposed method.

In experimental thin film physics, there is a demand to characterize a growing thin film or the thin film resulting from an experiment. While methods for discontinuous, island-like thin films have been developed, there is a lack of results directly applicable to semicontinuous thin film description. In this contribution, a unique combination of image processing methods is collected and further developed, which results in a novel set of semicontinuous thin film descriptors. In particular, the shape of the thin film contours and the thin film image intensity profiles are analyzed in a multiscale manner. The descriptiveness of the proposed features is demonstrated on a few thin film photographs from real experiments. This work establishes a basis for further measurement, description, simulation or other processing in the physics of semicontinuous thin films, using any direct imaging modality.