Motion blur acts on an image like a two dimensional low pass filter, whose spatial frequency characteristic depends both
on the trajectory of the relative motion between the scene and the camera and on the velocity vector variation along it.
When motion during exposure is permitted, the conventional, static notions of both the image exposure and the scene-toimage
mapping become unsuitable and must be revised to accommodate the image formation dynamics. This paper
develops an exact image formation model for arbitrary object-camera relative motion with arbitrary velocity profiles.
Moreover, for any motion the camera may operate in either continuous or flutter shutter exposure mode. Its result is a
convolution kernel, which is optimally designed for both the given motion and sensor array geometry, and hence permits
the most accurate computational undoing of the blurring effects for the given camera required in forensic and high
security applications. The theory has been implemented and a few examples are shown in the paper.
KEYWORDS: Camera shutters, Technetium, Spatial frequencies, Modulation transfer functions, Eye, Safety, Biometrics, Fourier transforms, Signal to noise ratio, Optical inspection
Acquiring iris or face images of moving subjects at larger distances using a flash to prevent the motion blur quickly runs
into eye safety concerns as the acquisition distance is increased. For that reason the flutter shutter method recently
proposed by Raskar et al.has generated considerable interest in the biometrics community. The paper concerns the design
of shutter sequences that produce the best images. The number of possible sequences grows exponentially in both the
subject' s motion velocity and desired exposure value, with their majority being useless. Because the exact solution leads
to an intractable mixed integer programming problem, we propose an approximate solution based on pre - screening the
sequences according to the distribution of roots in their Fourier transform. A very fast algorithm utilizing the Jury' s
criterion allows the testing to be done without explicitly computing the roots, making the approach practical for moderately
long sequences.
Arathorn developed a new theory to address the translation, rotation, scale and perspective invariance problem in vision.
According to it, both natural and machine vision systems may be built using a basic block which he calls the map-seeking
circuit. In his recent book1, he informally describes the circuit and a number of simulation studies to illustrate his
ideas and support his claims. In this paper, we complement his work by providing mathematical analysis of the circuit.
We first construct difference equations describing its dynamics and study when they converge to a steady state which
represents the circuit's interpretation of the input scene image. We then show that the state corresponds to the minimum
of an upper bound on the difference between the input image and its reconstruction done by the circuit using its built-in
banks of object memories and construction operators. The fact that the upper bound can be constructed and minimized
directly in a computationally efficient and numerically robust manner, without having to recourse to the map-seeking
circuit simulation, makes our alternative approach attractive for applications. We explain why the upper bound is not
always tight, which leads to the collusion and other matching errors noticed by Arathorn.
This paper first briefly describes the Laser Detection and Reciprocal Targeting (LDART) system being developed under the DARPA NEST program, whose purpose is to detect and locate enemy target designators. The system's sensor is an array of microelectronic (MEMS) detectors, each of which can measure the directional angle of incident light with a random error, whose distribution is known. The detector errors cause the sensor to perceive the source as if in a location that is generally different from its actual location. The paper's main contribution is to show how to optimally estimate the actual laser source location. We derive the probability distribution of perceived locations and show how it depends on both the source and sensor parameters. The distribution is then used to develop the maximum likelihood estimator of the actual source location, which allows to pinpoint the source with very good precision in spite of noisy measurements furnished by individual detectors.
Combat always involves uncertainty and uncertainty entails risk. To ensure that a combat task is prosecuted with the desired probability of success, the task commander has to devise an appropriate task force and then adjust it continuously in the course of battle. In order to do so, he has to evaluate how the probability of task success is related to the structure, capabilities and numerical strengths of combatants. For this purpose, predictive models of combat dynamics for combats in which the combatants fire asynchronously at random instants are developed from the first principles. Combats involving forces with both unlimited and limited ammunition supply are studied and modeled by stochastic Markov processes. In addition to the Markov models, another class of models first proposed by Brown was explored. The models compute directly the probability of win, in which we are primarily interested, without integrating the state probability equations. Experiments confirm that they produce exactly the same results at much lower computational cost.
The application of control and game theories to improve battle planning and execution requires models, which allow military strategists and commanders to reliably predict the expected outcomes of various alternatives over a long horizon into the future. We have developed probabilistic battle dynamics models, whose building blocks in the form of Markov chains are derived from the first principles, and applied them successfully in the design of the Model Predictive Task Commander package. This paper introduces basic concepts of our modeling approach and explains the probability distributions needed to compute the transition probabilities of the Markov chains.
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