High-level shape understanding and technique evaluation on large repositories of 3D shapes often benefit from additional information known about the shapes. One example of such information is the semantic segmentation of a shape into functional or meaningful parts. Generating accurate segmentations with meaningful segment boundaries is, however, a costly process, typically requiring large amounts of user time to achieve high quality results. In this paper we present an active learning framework for large dataset segmentation, which iteratively provides the user with new predictions by training new models based on already segmented shapes. Our proposed pipeline consists of three novel components. First, we a propose a fast and relatively accurate feature-based deep learning model to provide dataset-wide segmentation predictions. Second, we propose an information theory measure to estimate the prediction quality and for ordering subsequent fast and meaningful shape selection. Our experiments show that such suggestive ordering helps reduce users time and effort, produce high quality predictions, and construct a model that generalizes well. Finally, we provide effective segmentation refinement features to help the user quickly correct any incorrect predictions. We show that our framework is more accurate and in general more efficient than state-of-the-art, for massive dataset segmentation with while also providing consistent segment boundaries.
Entropy is a measure of uncertainty. It can be used to predict the probability of an event given some information. Entropy was first used in 3D geometry processing by @cite_33 , where it was used to estimate how much information was contained in a 3D surface. More recently, entropy has also been used for shape simplification @cite_27 , shape compression @cite_34 and to estimate the Saliency of a 3D shape @cite_35 . As we have no way of analyzing our model evaluation, we explored using entropy to rank the segmentation predictions, which to our knowledge has not been explored before for 3D shape analysis.
@cite_35 @cite_27 @cite_34 @cite_33
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Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems. Entropy has recently gained considerable significance as an important metric for network measurement. Previous research has shown its utility in clustering traffic and detecting traffic anomalies. While measuring the entropy of the traffic observed at a single point has already been studied, an interesting open problem is to measure the entropy of the traffic between every origin-destination pair. In this paper, we propose the first solution to this challenging problem. Our sketch builds upon and extends the Lp sketch of Indyk with significant additional innovations. We present calculations showing that our data streaming algorithm is feasible for high link speeds using commodity CPU memory at a reasonable cost. Our algorithm is shown to be very accurate in practice via simulations, using traffic traces collected at a tier-1 ISP backbone link. We use entropy ideas to study hard-core distributions on the independent sets of a finite, regular bipartite graph, specifically distributions according to which each independent set I is chosen with probability proportional to λ∣I∣ for some fixed λ > 0. Among the results obtained are rather precise bounds on occupation probabilities; a ‘phase transition’ statement for Hamming cubes; and an exact upper bound on the number of independent sets in an n-regular bipartite graph on a given number of vertices. We investigated long-range correlations in two literary texts, "Moby Dyck" by H. Melville and Grimm's tales. The analysis is based on the calculation of entropylike quantities as the mutual information for pairs of letters and the entropy, the mean uncertainty, per letter. We further estimate the number of different subwords of a given length n. Filtering out the contributions due to the effects of the finite length of the texts, we find correlations ranging to a few hundred letters. Scaling laws for the mutual information (decay with a power law), for the entropy per letter (decay with the inverse square root of n) and for the word numbers (stretched exponential growth with n and with a power law of the text length) were found.