ON COUNTING SEQUENCES AND SOME RESEARCH QUESTIONS

A counting sequence is a list of all binary words of the same length. Counting sequences of any fixed odd Hamming distance between successive words (codewords) are discussed. Gray codes are examples of counting sequences having a single-bit change between neighboring codewords. We describe some results on Gray codes and highlight some research questions. The spectrum of bit changes or transition counts for individual variables for some uniform counting sequences is considered. We show some recent minor findings and pose remaining open questions

A Zoomable Mapping of a Musical Parameter Space Using Hilbert Curves

The final publication is available at Computer Music Journal via http://dx.doi.org/10.1162/COMJ_a_0025

Binary pattern codification strategies in an active stereoscopic system based on flexible image guides

International audienceA wide variety of three dimensional (3D) measurement systems that can extract shape information's with sub millimetric accuracy is available in the industry. However, they generally are of macroscopic size and measuring on confined areas is not feasible. To miniaturize such systems, the step proposed is the integration of flexible image guides combined with compact optical probes. This miniaturization process is tested on an active stereoscopic measurement system. In the projection channel of the system, a digital micro-mirror device (DMD) generates structured binary patterns from an incoherent white light source and injects them into a first image guide. Then, a compact optical system projects the pattern on the measurement area. The same configuration principle is applied to the acquisition channel and allows the capture of the measurement area through a second image guide and finally to a digital camera. In this miniaturized system, image guides have lower resolution than in standard imaging devices. Indeed they are equivalent of 70k pixels devices to compare to the almost 800k pixels of the DMD and camera. That implies lower axial and lateral resolutions and consequently the shape reconstruction method must be carefully chosen. In this paper, several reconstruction strategies such as tuning the projected patterns frequency and also phase-shfit versus gray code based methods were compared considering the best axial resolution criteria

A fractal set from the binary reflected Gray code

The permutation associated with the decimal expression of the binary reflected Gray code with N bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of an IFS. For large values of N the set is examined from the point of view of time series analysis

Gray Codes and Symmetric Chains

We consider the problem of constructing a cyclic listing of all bitstrings of length 2n+1 with Hamming weights in the interval [n+1-l,n+l], where 1 = 12

Gray codes and symmetric chains

We consider the problem of constructing a cyclic listing of all bitstrings of length~$2n+1$ with Hamming weights in the interval $[n+1-\ell,n+\ell]$, where $1\leq \ell\leq n+1$, by flipping a single bit in each step. This is a far-ranging generalization of the well-known middle two levels problem (the case~$\ell=1$). We provide a solution for the case~$\ell=2$ and solve a relaxed version of the problem for general values of~$\ell$, by constructing cycle factors for those instances. Our proof uses symmetric chain decompositions of the hypercube, a concept known from the theory of posets, and we present several new constructions of such decompositions. In particular, we construct four pairwise edge-disjoint symmetric chain decompositions of the $n$-dimensional hypercube for any~$n\geq 12$

Sorting improves word-aligned bitmap indexes

Bitmap indexes must be compressed to reduce input/output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH) compression. These techniques are sensitive to the order of the rows: a simple lexicographical sort can divide the index size by 9 and make indexes several times faster. We investigate row-reordering heuristics. Simply permuting the columns of the table can increase the sorting efficiency by 40%. Secondary contributions include efficient algorithms to construct and aggregate bitmaps. The effect of word length is also reviewed by constructing 16-bit, 32-bit and 64-bit indexes. Using 64-bit CPUs, we find that 64-bit indexes are slightly faster than 32-bit indexes despite being nearly twice as large

Research 3D scanner for scanning of problematic surfaces

Práce se zabývá konstrukcí výzkumného 3D skeneru pro skenování problematických povrchů. Rešeršní část uvádí do problematiky 3D skenování a popisuje příčiny vzniku náhodných chyb. Dále obsahuje popis a rozdělení metod, které vedou k jejich eliminaci. Vlastní práce se pak zabývá návrhem a popisem hardwarové a softwarové části 3D skeneru. Výstupem práce je zařízení, které je schopné implementovat a srovnávat kvalitu kodifikačních metod zejména pro skenování problematických povrchů. Funkčnost zařízení byla ověřena experimentálním měřením.This diploma thesis deals with design of 3D scanner for scanning problematic surfaces. The research part introduces the problem of 3D scanning and describes causes of random errors. Further, it contains a description and division of methods that leads to their elimination. The practical part of the thesis deals with design and description of hardware and software parts of the 3D scanner. The output of this work is device that is able to implement and compare quality of codification methods mainly for scanning of problematic surfaces. The functionality of equipment was verified by experimental measurement.