Integrated 2-D Optical Flow Sensor

I present a new focal-plane analog VLSI sensor that estimates optical flow in two visual dimensions. The chip significantly improves previous approaches both with respect to the applied model of optical flow estimation as well as the actual hardware implementation. Its distributed computational architecture consists of an array of locally connected motion units that collectively solve for the unique optimal optical flow estimate. The novel gradient-based motion model assumes visual motion to be translational, smooth and biased. The model guarantees that the estimation problem is computationally well-posed regardless of the visual input. Model parameters can be globally adjusted, leading to a rich output behavior. Varying the smoothness strength, for example, can provide a continuous spectrum of motion estimates, ranging from normal to global optical flow. Unlike approaches that rely on the explicit matching of brightness edges in space or time, the applied gradient-based model assures spatiotemporal continuity on visual information. The non-linear coupling of the individual motion units improves the resulting optical flow estimate because it reduces spatial smoothing across large velocity differences. Extended measurements of a 30x30 array prototype sensor under real-world conditions demonstrate the validity of the model and the robustness and functionality of the implementation

Compact Integrated Transconductance Amplifier Circuit for Temporal Differentiation

A compact integrated CMOS circuit for temporal differentiation is presented. It consists of a high-gain inverting amplifier, an active non-linear transconductance and a capacitor and requires only 4 transistors in its minimal configuration.The circuit provides two rectified current outputs that are proportional to the temporal derivative of the input voltage signal. Besides the compactness of its design, the presented circuit is not dependent on the DC-value of the input signal, as compared with known integrated differentiator circuits. Measured chip results show that the circuit operates on a large input frequency range for which it provides nearideal temporal differentiation. The circuit is particularly suited for focal-plane implementations of gradient-based visual motion systems

Multifragmentation, Clustering, and Coalescence in Nuclear Collisions

Nuclear collisions at intermediate, relativistic, and ultra-relativistic energies offer unique opportunities to study in detail manifold fragmentation and clustering phenomena in dense nuclear matter. At intermediate energies, the well known processes of nuclear multifragmentation -- the disintegration of bulk nuclear matter in clusters of a wide range of sizes and masses -- allow the study of the critical point of the equation of state of nuclear matter. At very high energies, ultra-relativistic heavy-ion collisions offer a glimpse at the substructure of hadronic matter by crossing the phase boundary to the quark-gluon plasma. The hadronization of the quark-gluon plasma created in the fireball of a ultra-relativistic heavy-ion collision can be considered, again, as a clustering process. We will present two models which allow the simulation of nuclear multifragmentation and the hadronization via the formation of clusters in an interacting gas of quarks, and will discuss the importance of clustering to our understanding of hadronization in ultra-relativistic heavy-ion collisions.Comment: 10 pages, 8 figure

Combinatorial Proofs of Identities of Alzer and Prodinger and Some Generalizations

We provide combinatorial proofs of identities published by Alzer and Prodinger. These identities include that for integers b, n, and r with b ≥ 1 and n − 1 ≥ r ≥ 0 we have and for integers b, n, and r with b ≥ 0 and n − 1 ≥ r ≥ 0 we have Our combinatorial proofs generalize squares to sth powers, and involve generalized Eulerian numbers and generalized Delannoy numbers

An investigation of optimization techniques for drawing computer graphics displays

Techniques for reducing vector data plotting time are studied. The choice of tolerances in optimization and the application of optimization to plots produced on real time interactive display devices are discussed. All results are developed relative to plotting packages and support hardware so that results are useful in real world situations