Claude S. Lindquist

On implementing Kasa's circle fit procedure

This paper addresses the numerical issues of implementing Kasas circle fit procedure. We consider three main problems: (1) appropriateness of circle-fitting algorithm results to the measured data; (2) ambiguous circles due to the crowding of data; (3) data distribution along fitted circle for sensitivity improvement or measurement requirements. We seek to make noteworthy those elements of the circle fitting technique which contribute most to the accuracy (or inaccuracy) of the intended application. To that end, error bounds are derived and checks proposed to assess the applicability of the technique to the fitted data. Simulation results are submitted in support of the proposed methods.

Sensitivities of Band-Edge Selectivities

Many filters have a band-edge selectivity (BES) that is a function of parameters other than filter order. In these cases, the band-edge selectivity can be maximized without increasing the order of the filter. However, in increasing BES, we must keep track of the sensitivity of BES to the parameters. In this paper, we provide sensitivities of BES to filter parameters for a variety of classical filters, these being described by rational functions approximating the ideal filter magnitude response. The results are useful in the design of such filters.

On the construction of transitional filter nomographs

The construction of nomographs for transitional classical filters is described. Gain functions of classical filters are related to filter requirements resulting in a formulation for the general gain nomograph. The transitional filters that are products of approximating polynomials are incorporated into the general gain nomograph resulting in transitional filter nomographs that are sums of the individual nomographs. Nomographs for transitional filters using alternative forms where poles are interpolated are also considered. The resulting nomographs allow for quick optimization of transitional filter frequency response in many cases. Design examples are submitted and discussed. The proposed transitional filter nomographs provide the engineer with increased insight into the selection of classical transitional filters with optimum frequency response.

Sensitivity of the band-edge selectivity of various classical filters

Many filters have a band-edge selectivity (BES) that is a function of parameters other than filter order. When this is the case, the band-edge selectivity of these filters can be maximized without increasing their order. However, we must temper our intent by the sensitivity of the BES to the varying parameters. We study here the sensitivity of the band-edge selectivity of various classical filters, these being described by polynomials approximating the ideal brick-wall filter magnitude response.

Surface analysis algorithms for scanning probe microscopy

Abstract A single data set in scanning probe microscopy is large, typically in the megabyte range. As interpretation is accomplished by displaying the data in image form for visualization, image processing methods are used to both convert to visual images and to modify the images in order to clarify features of interest. Although an impressive number of image-processing algorithms are available on most commercial probe microscopes, many potentially very interesting ones are not. In addition, the special character of scanning probe data sets calls for development of new algorithms specially suited to this kind of problem. The work here analyzes images produced using atomic force microscope data sets. Algorithms are shown and discussed using images of oxide surfaces. The following algorithms are applied: tilt correction, scattering noise removal, surface smoothing, surface compression, probability density function analysis, correlation, and power spectrum analysis. Such algorithms and others serve to remove spurious surface spikes, enhance visualization of long-range surface features in the presence of short-range surface variations, remove line-to-line scanning artifacts, etc.

New edge detection algorithms based on adaptive estimation filters

In this paper we describe new edge detection algorithms based on adaptive two-dimensional estimation filters. Examples with the Lena image are used to illustrate our concepts.

Relationships Between Gain And Impulse Responses Of Matrix Filters

This paper summarizes some of the basic relationships be- tween gain and impulse responses of matrix filters, The im- pulse response matrix properties are defined in the time do- main. These matrices are then transformed into gain matri- ces in the frequency domain using generalized transforms.[1] A variety of time-generalized frequency relationships between these matrices are derived, Examples are presented to illustrate these results.

Selectivity nomographs for classical filters

Nomographs for determining the filter order of classical filters based on selectivity requirements are presented. The selectivities for a variety of standard classical filters are summarized in equation form and the general selectivity nomograph is constructed. The selectivity equations are then converted into nomograph form by applying the relationship between the transfer function and the response slope. Design examples are presented to demonstrate the usefulness of the selectivity nomographs. These nomographs can be used to gauge filter performance and combined with optimization techniques can yield superior classical filter designs.

Sensitivity of classical filter transfer functions

We present here the sensitivity of classical filter transfer functions that are polynomial approximations to the ideal brick-wall magnitude response. The transfer function is decomposed into the part corresponding to the passband ripple parameter and the approximating polynomial. It is shown that the sensitivity has a complementary transfer function response. With these sensitivity relations, it is possible to relate filter parameter variations to any part of the circuit implementing the transfer function. Examples are submitted and discussed to show the usefulness of these new results in providing a more thorough assessment of filter performance potential and limitations.

Locally adaptive orientation Wiener image filter with local noise estimate

The restoration of images degraded by additive noise has been addressed previously by several authors. In this work, to overcome the consequences that arise from cascading filters sequentially (namely, the fact that the noise behavior changes more and more the deeper into the cascade), while still preserving edges and maintaining low computational requirements, we propose a modified locally adaptive orientation Wiener filter (MAOW). Different masks are applied at each pixel to a local region and the mask yielding a minimum variance is the selected one; thus mask orientations can vary locally. In addition to improve the operation of the AOW, we need a noise estimation that is locally varying. This is obtained by using the information that is already available to us from the quantizer prior to filtering.