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The authors describe a coarse coding technique and present simulation results illustrating its usefulness and its limitations. Simulations show that a third-order neural network can be trained to distinguish between two objects in a 4096x4096 pixel input field independent of transformations in translation, in-plane rotation, and scale in less than ten passes through the training set. Furthermore, the authors empirically determine the limits of the coarse coding technique in the position, scale, and rotation invariant (PSRI) object recognition domain.

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Abstract.A nigher-order neural network (HONN) can be designed to be invariant to geometric transformations such as scale, translation, and in-plane rotation. Invariances are built directly into the arcnitecture of a HONN and do not need to be learned. Thus, for 2D object recognition, the network needs to be trained on just one View of each object class, not numerous scaled, translated, and rotated views. Because the 2D object recognition task is a component of the 3D object recognition task, built-in 2D invariance also decreases the size of the training set required for 3D object recognition. We present results for 2D object recognition both in simulation and within a robotic vision experiment and for 3D object recognition in simulation. We also compare our method to other approaches and show that HONNs have distinct advantages for position, scale, and rotation-invariant object recognition.The major drawback of HONNs is that the size of the input field is limited due to the memory required for the large number of interconnections in a fully connected network. We present partial connectivity strategies and a coarse-coding technique for overcoming this limitation and increasing the input field to that required by practical object recognition problems.

The emittance of an electron beam increases due to multiple scattering when passing through one or more thin foils. The effect of a given foil on a beam’s emittance is dependent on whether the beam is diverging, converging, or at a waist. A method for calculating the growth in emittance using betatron functions is presented. The technique provides a full description of the beam in phase space after a thin scatterer.

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Here we study the optical phase errors introduced into an optical correlator by the input and filter plane magneto-optic spatial light modulators. We measure and characterize the magnitude of these phase errors, evaluate their effects on the correlation results, and present a means of correction by a design modification of the binary phase-only optical-filter function. The efficacy of the phase-correction technique is quantified and is found to restore the correlation characteristics to those obtained in the absence of errors, to a high degree. The phase errors of other correlator system elements are also discussed and treated in a similar fashion.

A modified binary synthetic discriminant function filter designed to recognize objects over a range of rotated views has been verified on a laboratory optical correlator. A binary synthetic discriminant function filter has been previously described that will produce a specified correlation response for a set of training images. [See D. A. Jared and D. J. Ennis, "Inclusion of Filter Modulation in Synthetic-Discriminant-Function Construction," Appl. Opt. 28, 232-239 (1989).] In the filter design, the modulation characteristics of the device onto which the filter is mapped are included in the synthesis equations. The system of nonlinear equations is then solved using an iteration procedure based on the Newton-Raphson algorithm. The development of the filter-SDF (fSDF) method was driven by the practical concern to make currently available spatial light modulators with limited modulation capabilities functional for distortion invariant pattern recognition. This technique is used to synthesize filters for a binary magnetooptic spatial light modulator (MOSLM), the Sight-MOD produced by Semetex. Two MOSLMs are used in the laboratory correlator, one in the filter plane and one in the input plane. We demonstrate that a single filter produces equal correlation peaks for a sample object (a Shuttle Orbiter in these tests) over in-plane and out-of-plane rotation ranges up to 75 degrees . The correlator is able to track dynamically the shuttle as it moves along a curved path across the input field. Views of the object in between those in the training set are also recognized when training images are sufficiently close in angle (~5 degrees apart).