 

Visual Images Segmentation based on Uniform Textures Extraction
Goltsev, A. ; Gritsenko, V. ; Húsek, Dušan
A new effective procedure for partial texture segmentation of visual images is proposed. The procedure segments any input image into a number of nonoverlapping homogeneous negrained texture areas. The main advantages of the proposed procedure are as follows. It is completely unsupervised, that is, it processes the input image without any prior knowledge of either the type of textures or the number of texture segments in the image. In addition, the procedure segments arbitrary images of all types. This means that no changes to the procedure parameters are required to switch from one image type to another. Another major advantage of the procedure is that in most cases it extracts the uniform negrained texture segments present in the image, just as humans do. This result is supported by series of experiments that demonstrate the ability of the procedure to delineate uniform negrained texture segments over a wide range of images. At a minimum, image processing according to the proposed technique leads to a signficant reduction in the uncertainty of the internal structure of the analyzed image.


City simulation software for modeling, planning, and strategic assessment of territorial city units
Svítek, M. ; Přibyl, O. ; Vorel, J. ; Garlík, B. ; Resler, Jaroslav ; Kozhevnikov, S. ; Krč, Pavel ; Geletič, Jan ; Daniel, Milan ; Dostál, R. ; Janča, T. ; Myška, V. ; Aralkina, O. ; Pereira, A. M.
SVÍTEK, M., PŘIBYL, O., VOREL, J., GARLÍK, B., RESLER, J., KOZHEVNIKOV, S., KRČ, P., GELETIČ, J., DANIEL, M., DOSTÁL, R., JANČA, T., MYŠKA, V., ARALKINA, O., PEREIRA, A. M. City simulation software for modeling, planning, and strategic assessment of territorial city units. 1.1. Prague: CTU & ICS CAS, 2021. Technical Report. ABSTRACT: The Smart Resilience City concept is a new vision of a city as a digital platform and ecosystem of smart services where agents of people, things, documents, robots, and other entities can directly negotiate with each other on resource demand principals providing the best possible solution. It creates the smart environment making possible selforganization in sustainable or, when needed, resilient way of individuals, groups and the whole system objectives.


Lineartime Algorithms for Largest Inscribed Quadrilateral
Keikha, Vahideh
Let P be a convex polygon of n vertices. We present a lineartime algorithm for the problem of computing the largestarea inscribed quadrilateral of P. We also design the parallel version of the algorithm with O(log n) time and O(n) work in CREW PRAM model, which is quite work optimal. Our parallel algorithm also computes all the antipodal pairs of a convex polygon with O(log n) time and O(log2n+s) work, where s is the number of antipodal pairs, that we hope is of independent interest. We also discuss several approximation algorithms (both constant factor and approximation scheme) for computing the largestinscribed kgons for constant values of k, in both area and perimeter measures.
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Two limitedmemory optimization methods with minimum violation of the previous quasiNewton equations
Vlček, Jan ; Lukšan, Ladislav
Limitedmemory variable metric methods based on the wellknown BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey (1991) and Vlček and Lukšan (2019), satisfies the quasiNewton equations with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the quasiNewton equations as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously combined with methods based on vector corrections for conjugacy (Vlček and Lukšan, 2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods.
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Sort Program for Real Keys with Linear Time Complexity
Jiřina, Marcel
In this report we present a program for sorting data structures with sorting keys as real numbers, i.e. of type "real" or "float". The basis of the program is a modification of the countingsort algorithm for reals (instead of integers). It uses a comparisiontype sorting for small part of data set given. The time complexity of this part of program can be bounded by linear function of n and thus, the total time complexity is also O(n) for n data items.
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Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?
Rohn, Jiří
We consider the conjecture formulated in the title concerning existence of a symmetric singular matrix in a singular symmetric interval matrix. We show by means of a counterexample that it is generally not valid, and we prove that it becomes true under an additional assumption of positive semide niteness of the midpoint matrix. The proof is constructive.
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A Logical Characteristic of ReadOnce Branching Programs
Žák, Stanislav
We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two appropriate properties: i) The ”knowledge” arising at a stage of computation in question is derivable from the ”knowledge” arising at the previous stage according to the rules of the model and according to the local arrangement of the b.p. ii) The model confirms the intuitively wellknown fact that the knowledge arising at a node of a computation depends not only on it but in some cases also on a ”mystery” information. (I. e. different computations reaching the same node may have different knowledge(s) arisen at it.) We prove that with respect to our model no such information exists in readonce b.p.‘s but on the other hand in b. p.‘s which are not readonce such information must be present. The readonce property forms a frontier. More concretely, we may see the instances of our models as a systems S = (U,D) where U is a universe of knowledge and D are derivation rules. We say that a b.p. P is compatible with a system S iff along each computation in P S derives F (false) or T (true) at the end correctly according to the label of the reached sink. This key notion modifies the classic paradigm which takes the computational complexity with respect to different classes of restricted b.p.‘s (e.g. readonce b.p.‘s, kb.p.‘s, b.p.‘s computing in limited time etc.). Now, the restriction is defined by a subset of systems and only these programs are taken into account which are compatible with at least one of the chosen systems. Further we understand the sets U of knowledge(s) as a sets of admissible logical formulae. It is clear that more rich sets U‘s imply the large restrictions on b.p.‘s and consequently the smaller complexities of Boolean functions are detected. More rich logical equipment implies stronger computational effectiveness. Another question arises: given a set of Boolean functions (e.g. codes of some graphs) what logical equipment is optimal from the point of complexity?
