Model-based machine learning methods incorporate domain knowledge from the physical forward model of an inverse problem to reduce the need for training data. In this research, we show how this can be used to address challenging limitations such as occlusion. We combine a convolutional neural network with a novel computational reconstruction method that combines source and attenuation distributions in order to model occlusion. We demonstrate the ability to quickly learn to address reconstruction artifacts and opacity, forming a significantly improved final image of the scene based on as little as a single training image. The algorithm can be implemented efficiently and scaled to large problem sizes.
Spectacle lenses are an important application of freeform manufacturing, with complex designs such as progressive lenses requiring nontraditional and specialized surface shapes. Such lenses also pose special challenges for optical design, as the eye’s gaze constantly changes relative to the lens. At the same time, many applications require sacrificing one region, such as the transition in a smooth bifocal, while achieving high quality in other regions. Common representations of freeform lens surfaces using polynomials or splines are poorly suited for such requirements. We describe an approach to optimize freeform spectacle lenses using a nonparametric representation of the surfaces at high resolution. Requirements for smoothness are quantified in terms of high-order aberrations. This allows us to describe spatial variations in the design while also incorporating a constraint for optical smoothness and manufacturability. We show how this can be formulated as a regularized optimization problem incorporating raytracing, which can be solved efficiently. The approach can be used to design various kinds of lenses including progressive, bifocal, and lenticular designs. The designs have been successfully manufactured on multiple different brands of freeform generators. Manufactured lenses are found to perform as designed, including without polishing when supported by the material and generator.
Accurately measuring optical aberrations is an important process for several eyecare tasks. Managing the individual variations found in human eyes plays a large role in properly defining these aberrations. A common method to measure optical aberrations uses sensors to locally capture the gradients across a grid of points. This data is used to reconstruct the wavefront resulting from light passing through the eye. In using this method of measurement, typical individual variations such as scarring or eyelashes can lead to shortcomings in the data. These shortcomings can manifest as noise or even areas of entirely missing data. The use of ANN (artificial neural networks) is one way to minimize the effects of these unpredictable deviations. In this work, ANN’s were used to determine higher order Zernike coefficients based on coordinates and gradients of the wavefront at those locations. To accomplish this, different ANN architectures were evaluated using sets of ideal inputs to establish the best performing baseline model. This baseline model was then compared with models that were trained under varying conditions created by incorporating deviations from ideal samples. By training neural networks using variable quality data, models can be created to reconstruct wavefronts and account for these conditions. This in turn, can lead to useful applications when measuring for aberrations resulting from the eye.
We consider a data-driven approach for the subdivision of an individual subject's functional Magnetic Resonance Imaging (fMRI) scan into regions of interest, i.e., brain parcellation. The approach is based on a computational technique for calculating resolution from inverse problem theory, which we apply to neighborhood selection for brain connectivity networks. This can be efficiently calculated even for very large images, and explicitly incorporates regularization in the form of spatial smoothing and a noise cutoff. We demonstrate the reproducibility of the method on multiple scans of the same subjects, as well as the variations between subjects.
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