Randomly removing g handles at once

AbstractIndyk and Sidiropoulos (2007) proved that any orientable graph of genus g can be probabilistically embedded into a graph of genus g−1 with constant distortion. Viewing a graph of genus g as embedded on the surface of a sphere with g handles attached, Indyk and Sidiropoulos' method gives an embedding into a distribution over planar graphs with distortion 2O(g), by iteratively removing the handles. By removing all g handles at once, we present a probabilistic embedding with distortion O(g2) for both orientable and non-orientable graphs. Our result is obtained by showing that the minimum-cut graph of Erickson and Har-Peled (2004) has low dilation, and then randomly cutting this graph out of the surface using the Peeling Lemma of Lee and Sidiropoulos (2009)

Speech Processing in Computer Vision Applications

Deep learning has been recently proven to be a viable asset in determining features in the field of Speech Analysis. Deep learning methods like Convolutional Neural Networks facilitate the expansion of specific feature information in waveforms, allowing networks to create more feature dense representations of data. Our work attempts to address the problem of re-creating a face given a speaker\u27s voice and speaker identification using deep learning methods. In this work, we first review the fundamental background in speech processing and its related applications. Then we introduce novel deep learning-based methods to speech feature analysis. Finally, we will present our deep learning approaches to speaker identification and speech to face synthesis. The presented method can convert a speaker audio sample to an image of their predicted face. This framework is composed of several chained together networks, each with an essential step in the conversion process. These include Audio embedding, encoding, and face generation networks, respectively. Our experiments show that certain features can map to the face and that with a speaker\u27s voice, DNNs can create their face and that a GUI could be used in conjunction to display a speaker recognition network\u27s data