Feature Point Detection and Curve Approximation for Early Processing of Freehand Sketches

Freehand sketching is both a natural and crucial part of design, yet is unsupported by current design automation software. We are working to combine the flexibility and ease of use of paper and pencil with the processing power of a computer to produce a design environment that feels as natural as paper, yet is considerably smarter. One of the most basic steps in accomplishing this is converting the original digitized pen strokes in the sketch into the intended geometric objects using feature point detection and approximation. We demonstrate how multiple sources of information can be combined for feature detection in strokes and apply this technique using two approaches to signal processing, one using simple average based thresholding and a second using scale space.

ADAM: A Decentralized Parallel Computer Architecture Featuring Fast Thread and Data Migration and a Uniform Hardware Abstraction

The furious pace of Moore's Law is driving computer architecture into a realm where the the speed of light is the dominant factor in system latencies. The number of clock cycles to span a chip are increasing, while the number of bits that can be accessed within a clock cycle is decreasing. Hence, it is becoming more difficult to hide latency. One alternative solution is to reduce latency by migrating threads and data, but the overhead of existing implementations has previously made migration an unserviceable solution so far. I present an architecture, implementation, and mechanisms that reduces the overhead of migration to the point where migration is a viable supplement to other latency hiding mechanisms, such as multithreading. The architecture is abstract, and presents programmers with a simple, uniform fine-grained multithreaded parallel programming model with implicit memory management. In other words, the spatial nature and implementation details (such as the number of processors) of a parallel machine are entirely hidden from the programmer. Compiler writers are encouraged to devise programming languages for the machine that guide a programmer to express their ideas in terms of objects, since objects exhibit an inherent physical locality of data and code. The machine implementation can then leverage this locality to automatically distribute data and threads across the physical machine by using a set of high performance migration mechanisms. An implementation of this architecture could migrate a null thread in 66 cycles -- over a factor of 1000 improvement over previous work. Performance also scales well; the time required to move a typical thread is only 4 to 5 times that of a null thread. Data migration performance is similar, and scales linearly with data block size. Since the performance of the migration mechanism is on par with that of an L2 cache, the implementation simulated in my work has no data caches and relies instead on multithreading and the migration mechanism to hide and reduce access latencies.

Measure Fields for Function Approximation

The computation of a piecewise smooth function that approximates a finite set of data points may be decomposed into two decoupled tasks: first, the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist on the sets of points best approximated by each model, and second, the computation of the normalized discriminant functions for each induced class. The approximating function may then be computed as the optimal estimator with respect to this measure field. We give an efficient procedure for effecting both computations, and for the determination of the optimal number of components.

An Equivalence Between Sparse Approximation and Support Vector Machines

In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem.

Convergence Rates of Approximation by Translates

In this paper we consider the problem of approximating a function belonging to some funtion space Φ by a linear comination of n translates of a given function G. Ussing a lemma by Jones (1990) and Barron (1991) we show that it is possible to define function spaces and functions G for which the rate of convergence to zero of the erro is 0(1/n) in any number of dimensions. The apparent avoidance of the "curse of dimensionality" is due to the fact that these function spaces are more and more constrained as the dimension increases. Examples include spaces of the Sobolev tpe, in which the number of weak derivatives is required to be larger than the number of dimensions. We give results both for approximation in the L2 norm and in the Lc norm. The interesting feature of these results is that, thanks to the constructive nature of Jones" and Barron"s lemma, an iterative procedure is defined that can achieve this rate.