I will described a nonparametric framework for locally adaptive signal processing and analysis. This framework is based upon the notion of Kernel Regression which we generalize to adapt to local characteristics of the given data, resulting in descriptors which take into account both the spatial density of the samples (“the geometry”), and the actual values of those samples (“the radiometry”). These descriptors are exceedingly robust in capturing the underlying structure of the signals even in the presence of significant noise, missing data, and other disturbances. As the framework does not rely upon strong assumptions about noise or signal models, it is applicable to a wide variety of problems. On the processing side, I will illustrate examples in two and three dimensions including state of the art denoising, upscaling, and deblurring. On the analysis side, I will describe the application of the framework to training-free object detection in images, and action detection in video, from a single example.
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