Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

The Alignment of Objects With Smooth Surfaces: Error Analysis of the Curvature Method

The recognition of objects with smooth bounding surfaces from their contour images is considerably more complicated than that of objects with sharp edges, since in the former case the set of object points that generates the silhouette contours changes from one view to another. The "curvature method", developed by Basri and Ullman [1988], provides a method to approximate the appearance of such objects from different viewpoints. In this paper we analyze the curvature method. We apply the method to ellipsoidal objects and compute analytically the error obtained for different rotations of the objects. The error depends on the exact shape of the ellipsoid (namely, the relative lengths of its axes), and it increases a sthe ellipsoid becomes "deep" (elongated in the Z-direction). We show that the errors are usually small, and that, in general, a small number of models is required to predict the appearance of an ellipsoid from all possible views. Finally, we show experimentally that the curvature method applies as well to objects with hyperbolic surface patches.

On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions

In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show that the total generalization error is partly due to the insufficient representational capacity of the network (because of its finite size) and partly due to insufficient information about the target function (because of finite number of samples). We make several observations about generalization error which are valid irrespective of the approximation scheme. Our result also sheds light on ways to choose an appropriate network architecture for a particular problem.

Error Detection and Recovery for Robot Motion Planning with Uncertainty

Robots must plan and execute tasks in the presence of uncertainty. Uncertainty arises from sensing errors, control errors, and uncertainty in the geometry of the environment. The last, which is called model error, has received little previous attention. We present a framework for computing motion strategies that are guaranteed to succeed in the presence of all three kinds of uncertainty. The motion strategies comprise sensor-based gross motions, compliant motions, and simple pushing motions.

An Analysis of the Effect of Gaussian Error in Object Recognition

Object recognition is complicated by clutter, occlusion, and sensor error. Since pose hypotheses are based on image feature locations, these effects can lead to false negatives and positives. In a typical recognition algorithm, pose hypotheses are tested against the image, and a score is assigned to each hypothesis. We use a statistical model to determine the score distribution associated with correct and incorrect pose hypotheses, and use binary hypothesis testing techniques to distinguish between them. Using this approach we can compare algorithms and noise models, and automatically choose values for internal system thresholds to minimize the probability of making a mistake.

Nanocrystalline Ge Flash Memories: Electrical Characterization and Trap Engineering

Conventional floating gate non-volatile memories (NVMs) present critical issues for device scalability beyond the sub-90 nm node, such as gate length and tunnel oxide thickness reduction. Nanocrystalline germanium (nc-Ge) quantum dot flash memories are fully CMOS compatible technology based on discrete isolated charge storage nodules which have the potential of pushing further the scalability of conventional NVMs. Quantum dot memories offer lower operating voltages as compared to conventional floating-gate (FG) Flash memories due to thinner tunnel dielectrics which allow higher tunneling probabilities. The isolated charge nodules suppress charge loss through lateral paths, thereby achieving a superior charge retention time. Despite the considerable amount of efforts devoted to the study of nanocrystal Flash memories, the charge storage mechanism remains obscure. Interfacial defects of the nanocrystals seem to play a role in charge storage in recent studies, although storage in the nanocrystal conduction band by quantum confinement has been reported earlier. In this work, a single transistor memory structure with threshold voltage shift, Vth, exceeding ~1.5 V corresponding to interface charge trapping in nc-Ge, operating at 0.96 MV/cm, is presented. The trapping effect is eliminated when nc-Ge is synthesized in forming gas thus excluding the possibility of quantum confinement and Coulomb blockade effects. Through discharging kinetics, the model of deep level trap charge storage is confirmed. The trap energy level is dependent on the matrix which confines the nc-Ge.