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Interpreting an image as a function on a compact subset of the Euclidean plane, we get its scale-space by diffusion, spreading the image over the entire plane. This generates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian kernel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero...
The need to prolong the ability for older adults to live at home independently has become an important area of smart environment research. In this proposal, we demonstrate a web-based visualization system (CASASviz) that integrates monitoring, analysis, and automated recognition of residents behavior patterns in smart environments. In our data collection module, we collect real sensor data from the...
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