Weighted Radon transforms for which the Chang approximate inversion formula is precise

We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given

The flip-graph of the 4-dimensional cube is connected

Flip-graph connectedness is established here for the vertex set of the 4-dimensional cube. It is found as a consequence that this vertex set has 92 487 256 triangulations, partitioned into 247 451 symmetry classes.Comment: 20 pages, 3 figures, revised proofs and notation

A uniform reconstruction formula in integral geometry

A general method for analytic inversion in integral geometry is proposed. All classical and some new reconstruction formulas of Radon-John type are obtained by this method. No harmonic analysis and PDE is used

MinMax Radon Barcodes for Medical Image Retrieval

Content-based medical image retrieval can support diagnostic decisions by clinical experts. Examining similar images may provide clues to the expert to remove uncertainties in his/her final diagnosis. Beyond conventional feature descriptors, binary features in different ways have been recently proposed to encode the image content. A recent proposal is "Radon barcodes" that employ binarized Radon projections to tag/annotate medical images with content-based binary vectors, called barcodes. In this paper, MinMax Radon barcodes are introduced which are superior to "local thresholding" scheme suggested in the literature. Using IRMA dataset with 14,410 x-ray images from 193 different classes, the advantage of using MinMax Radon barcodes over \emph{thresholded} Radon barcodes are demonstrated. The retrieval error for direct search drops by more than 15\%. As well, SURF, as a well-established non-binary approach, and BRISK, as a recent binary method are examined to compare their results with MinMax Radon barcodes when retrieving images from IRMA dataset. The results demonstrate that MinMax Radon barcodes are faster and more accurate when applied on IRMA images.Comment: To appear in proceedings of the 12th International Symposium on Visual Computing, December 12-14, 2016, Las Vegas, Nevada, US

On the Tomographic Picture of Quantum Mechanics

We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive-definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics.Comment: 10 pages,latex,submitted to Physics Letters

Kopyor Coconut Detection Using Sound-based Dynamic TIME Warping Method

Kopyor coconut is a coconut that has genetic abnormalities which cause the coconut meat to have a unique texture and is detached from the coconut shell. Its uniqueness attracts many enthusiasts resulting in a high economic value, 4-5 times that of the ordinary coconut. From its external appearance, kopyor coconut does not differ with ordinary coconut and this poses a challenge in the detection stage. To date, both farmers and sellers use a traditional approach by listening to the sound of whisk from kopyor coconut to detect them. Unfortunately, this approach relies heavily on experience and expertise of the person. Therefore, a new detection approach is proposed based on sound recognition using Mel Frequency Cepstrum Coefficient (MFCC) as the method for feature extraction and Dynamic Time Warping (DTW) as the method for feature matching. Objects that will be detected are kopyor coconuts and ordinary coconut which has grown mature. By implementing both methods, a program has been developed to detect kopyor coconut with an accuracy of 93.8%