On universal partial words

A universal word for a finite alphabet $A$ and some integer $n\geq 1$ is a word over $A$ such that every word in $A^n$ appears exactly once as a subword (cyclically or linearly). It is well-known and easy to prove that universal words exist for any $A$ and $n$. In this work we initiate the systematic study of universal partial words. These are words that in addition to the letters from $A$ may contain an arbitrary number of occurrences of a special `joker' symbol $\Diamond\notin A$, which can be substituted by any symbol from $A$. For example, $u=0\Diamond 011100$ is a linear partial word for the binary alphabet $A=\{0,1\}$ and for $n=3$ (e.g., the first three letters of $u$ yield the subwords $000$ and $010$). We present results on the existence and non-existence of linear and cyclic universal partial words in different situations (depending on the number of $\Diamond$s and their positions), including various explicit constructions. We also provide numerous examples of universal partial words that we found with the help of a computer

Fusion of LIDAR with stereo camera data - an assessment

This thesis explores data fusion of LIDAR (laser range-finding) with stereo matching, with a particular emphasis on close-range industrial 3D imaging. Recently there has been interest in improving the robustness of stereo matching using data fusion with active range data. These range data have typically been acquired using time of flight cameras (ToFCs), however ToFCs offer poor spatial resolution and are noisy. Comparatively little work has been performed using LIDAR. It is argued that stereo and LIDAR are complementary and there are numerous advantages to integrating LIDAR into stereo systems. For instance, camera calibration is a necessary prerequisite for stereo 3D reconstruction, but the process is often tedious and requires precise calibration targets. It is shown that a visible-beam LIDAR enables automatic, accurate (sub-pixel) extrinsic and intrinsic camera calibration without any explicit targets. Two methods for using LIDAR to assist dense disparity maps from featureless scenes were investigated. The first involved using a LIDAR to provide high-confidence seed points for a region growing stereo matching algorithm. It is shown that these seed points allow dense matching in scenes which fail to match using stereo alone. Secondly, LIDAR was used to provide artificial texture in featureless image regions. Texture was generated by combining real or simulated images of every point the laser hits to form a pseudo-random pattern. Machine learning was used to determine the image regions that are most likely to be stereo- matched, reducing the number of LIDAR points required. Results are compared to competing techniques such as laser speckle, data projection and diffractive optical elements

Robust Positioning Patterns with Low Redundancy

A robust positioning pattern is a large array that allows a mobile device to locate its position by reading a possibly corrupted small window around it. In this paper, we provide constructions of binary positioning patterns, equipped with efficient locating algorithms, that are robust to a constant number of errors and have redundancy within a constant factor of optimality. Furthermore, we modify our constructions to correct rank errors and obtain binary positioning patterns robust to any errors of rank less than a constant number. Additionally, we construct $q$-ary robust positioning sequences robust to a large number of errors, some of which have length attaining the upper bound. Our construction of binary positioning sequences that are robust to a constant number of errors has the least known redundancy amongst those explicit constructions with efficient locating algorithms. On the other hand, for binary robust positioning arrays, our construction is the first explicit construction whose redundancy is within a constant factor of optimality. The locating algorithms accompanying both constructions run in time cubic in sequence length or array dimension.Comment: Extended Version of SODA 2019 Pape

LWA 2013. Lernen, Wissen & Adaptivität ; Workshop Proceedings Bamberg, 7.-9. October 2013

LWA Workshop Proceedings: LWA stands for "Lernen, Wissen, Adaption" (Learning, Knowledge, Adaptation). It is the joint forum of four special interest groups of the German Computer Science Society (GI). Following the tradition of the last years, LWA provides a joint forum for experienced and for young researchers, to bring insights to recent trends, technologies and applications, and to promote interaction among the SIGs