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Multiresolution has been extensively used in many areas of computer science, including biometrics. We introduce local multiresolution filters for quadratic and cubic B-splines that satisfy the first and the second level of smoothness respectively. For constructing these filters, we use a reverse subdivision method. We also show how to use and extend these filters for tensor-product surfaces, and 2D/3D images. For some types of data, such as curves and surfaces, boundary interpolation is strongly desired. To maintain this condition, we introduce extraordinary filters for boundaries. For images and other cases in which interpolating the boundaries is not required or even desired, we need a particular arrangement to be able to apply regular filters. As a solution, we propose a technique based on symmetric extension. Practical issues for efficient implementation of multiresolution are discussed. Finally, we discuss some example applications in biometrics, including iris synthesis and volumetric data visualization.

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Determining similarity of two point sequences (strokes) is a fundamental task in gestural interfaces. Because the length of each stroke is arbitrary, mapping to a fixed-dimension feature space is often done to allow for direct comparison. In this paper, we propose a new feature space based on angle quantization. For each adjacent pair of points in a stroke, the vector between them defines an angle relative to a fixed axis. The sequence of these angles can be mapped to a kdimensional feature space by quantizing the unit circle into k ranges, and taking a normalized count of the number of stroke angles in each range. The Euclidean distance between strokes in this feature space gives a measure of stroke similarity. The measure is scale invariant, and some degree of rotational invariance can be achieved with slight modification. Our method is shown to offer efficient and accurate gestural matching performance compared to traditional signal-processing and image-based methods.

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