2016/2

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    A tabu search approach for the reconstruction of binary images without empty interior region
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2016) Billionnet, A.; Jarray, F.; Tlig, G.; Zagrouba, E.
    In this paper, we are concerned with a discrete tomography problem. We seek to reconstruct a binary image from its orthogonal projections, i.e, its horizontal and vertical line sums without interior black holes. We provide a tabu search approach to minimize the number of holes while satisfying the projections. We test our approach on some random binary images. Computational results show that the algorithm proposed produces near-optimal solutions for all test problems.
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    North Atlantic right whale localization and recognition using very deep and leaky Neural Network
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2016) Kabani, A.; El-Sakka, M. R.
    We describe a deep learning model that can be used to recognize individual right whales in aerial images. We developed our model using a data set provided by the National Oceanic and Atmospheric Administration. The main challenge we faced when working on this data set is that the size of the training set is very small (4,544 images) with some classes having only 1 image. While this data set is by far the largest of its kind, it is very di cult to train a deep neural network with such a small data set. However, we were able to overcome this challenge by dividing this problem into smaller tasks and by reducing the viewpoint variance in the data set. First, we localize the body and the head of the whale using deep learning. Then, we align the whale and normalize it with respect to rotation. Finally, a network is used to recognize the whale by analyzing its callosities. The top-1 accuracy of the model is 69.7% and the top-5 accuracy is 85%. The solution we describe in this paper was ranked 5th (out of 364 teams) in a challenge to solve this problem.
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    A modified Block Matching 3D algorithm for additive noise reduction
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2016) Alkinani, M. H.; El-Sakka, M. R.
    This paper presents a patch-based image ltering algorithm for addi- tive noise reduction. Our algorithm is a modi cation to the block matching 3D algorithm, where an adaptive thresholding was used for the collaborative hard- thresholding step. The collaborative Wiener ltering step was also modi ed by assigning more weights for similar patches. Experimental results show that our algorithm outperforms the original block matching 3D algorithm at various noise levels.
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    Mathematics for applications in imaging – foreword
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2016) Brimkov, V. E.; Barneva, R. P.
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    On Farey table and its compression for space optimization with guaranteed error bounds
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2016) Paria, B.; Pratihar, S.; Bhowmick, P.
    Farey sequences, introduced by such renowned mathematicians as John Farey, Charles Haros, and Augustin-L. Cauchy over 200 years ago, are quite well- known by today in theory of fractions, but its computational perspectives are pos- sibly not yet explored up to its merit. In this paper, we present some novel theoret- ical results and e cient algorithms for representation of a Farey sequence through a Farey table. The ranks of the fractions in a Farey sequence are stored in the Farey table to provide an e cient solution to the rank problem, thereby aiding in and speeding up any application frequently requiring fraction ranks for computational speed-up. As the size of the Farey sequence grows quadratically with its order, the Farey table becomes inadvertently large, which calls for its (lossy) compression up to a permissible error. We have, therefore, proposed two compression schemes to obtain a compressed Farey table (CFT). The necessary analysis has been done in detail to derive the error bound in a CFT. As the nal step towards space opti- mization, we have also shown how a CFT can be stored in a 1-dimensional array. Experimental results have been furnished to demonstrate the characteristics and e ciency of a Farey table and its compressed form.