In many inverse problems with prior information, the measurement residual and the reconstruction error are two natural metrics for reconstruction quality, where the measurement residual is defined as the weighted sum of the squared differences between the data actually measured and the data predicted by the reconstructed model, and the reconstruction error is defined as the sum of the squared differences between the reconstruction and the truth, averaged over some a priori probability space of possible solutions. A reconstruction method that minimizes only one of these cost functions may produce unacceptable results on the other. This paper develops reconstruction methods that control both residual and error, achieving the minimum residual for any fixed error or vice versa. These jointly optimal estimators can be obtained by minimizing a weighted sum of the residual and the error; the weights are determined by the slope of the tradeoff curve at the desired point and may be determined iteratively. These results generalize to other cost functions, provided that the cost functions are quadratic and have unique minimizers; some results are obtained under the weaker assumption that the cost functions are convex.
The video recording of dynamic experiments using infrared thermography can produce large numbers of images. Ten seconds of video includes 300 frames, each of may contain useful information. Automation is necessary to reduce the analysis time to an acceptable level. Since each experiment will have its own unique characteristics, the development of custom software for each analysis by a professional programmer is unreasonably expensive. A better approach is to implement a programmable interface to a general-purpose analysis program which the experimenter can program for a specific analyses needed. Version 3 of the Video Data Analysis System (VDAS) incorporates such an interface. In addition to standard programming language commands for arithmetic, input/output and flow to control, VDAS includes facilities for image processing, quantitative temperature and emissivity measurement, scanner calibration, noise and artifact reduction, and temperature contouring. An on-line help system describes the available commands or helps the user find the right command for a particular purpose. Additional commands allow the user to control a video disk player and recording for automatic processing of complete video sequences.
Digital image processing has been used to measure projectile velocity and spin rate from pairs of synchro-ballistic camera images. Two cameras displaced along the flight path are used. Each image contains the projectile image and timing marks to determine the time scale. Both cameras use the same timing generator allowing a common timing mark denoting the same instant to be defined in both images. Velocity is determined from the actual projectile length the length in the image and the time scale. A circumferential sawtooth pattern painted on the projectile is used to determine the rotation angle in each of the two images. The distance between the common timing mark and the. projectile tip is used to determine the time at which the projectile passes each camera. The spin rate is computed as the angle difference divided by the time difference. The user interface is organized as a computer spreadsheet input values may be entered in any order. The operator recognizes the key points in the image and digitizes their coordinates using an operator-controlled trackball. Interactive contrast enhancement image scrolling and zoom are provided. The measurement accuracy is comparable to manual methods but the time required is significantly reduced.
An infrared scanner which is good for visual inspection is not always suitable for image processing applications.
Noise and artifacts which are inconspicuous in continuous video can become objectionable when a single frame is
digitized, processed and displayed. Fortunately, image processing can often be used to reduce or eliminate the
artifacts.
Signal noise and video interference can be reduced by a spatial lowpass filter; the filter can be tuned to the
interference frequency to eliminate it completely. Digitizing an interlaced scan of a rapidly-changing scene effectively
superimposes two images at slightly different instants; this image can be split into two images with reduced spatial
resolution but twice the time resolution. The use of an oscillating mirror for scanning can introduce a ragged
appearance on edges in the scene; this artifact can be greatly reduced by a suitable filter design.
If the images are to be used for quantitative temperature or radiance measurements, then care must be taken
to ensure that the filter algorithms do not introduce any systematic bias or distortion and that they do not move
significant peaks and edges in the image. It is shown that a linear filter is well-behaved in this sense provided that
its impulse response is localized, even, and has unit area.
A filter matched to the characteristics of a specific equipment configuration was designed, implemented, and
tested on sample images from that equipment. Selected sample images are shown before and after processing.
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