Sampling Shape Contours Using Optimization over a Geometric Graph

Abstract

Consider selecting points on a contour in the x-y plane. In shape analysis, this is frequently referred to as contour sampling. It is important to select the points such that they effectively represent the shape of the contour. Generally, the stroke order and number of strokes are informative for that purpose. Several effective methods exist for sampling contours drawn with a certain stroke order and number of strokes, such as the English alphabet or Arabic figures. However, many contours entail an uncertain stroke order and number of strokes, such as pictures of symbols, and little research has focused on methods for sampling such contours. This is because selecting the points in this case typically requires a large computational cost to check all the possible choices. In this paper, we present a sampling method that is useful regardless of whether the contours are drawn with a certain stroke order and number of strokes or not. Our sampling method thereby expands the application possibilities of contour processing. We formulate contour sampling as a discrete optimization problem that can be solved using a type of direct search. Based on a geometric graph whose vertices are the points and whose edges form rectangles, we construct an effective objective function for the problem. Using different shape datasets, we demonstrate that our sampling method is effective with respect to shape representation and retrieval.

Fast Piecewise Polynomial Fitting of Time-Series Data for Streaming Computing

“…In recent years, researchers have shown an intensive research in approximate representation or compression of large-scale data. The most popular methods include Singular Value Decomposition (SVD) [3]- [7], Discrete Fourier Transform (DFT) [8]- [11], Discrete Wavelet Transform (DWT) [5], [12]- [15], Piecewise Aggregation Approximation (PAA) [16]- [18], Piecewise Linear Approximation (PLA) [1], [2], [19]- [23], Adaptive Piecewise Constant Approximation (APCA) [24]- [26], Piecewise Curve Fitting [27]- [38], and some other methods [39]. Piecewise curve fitting fits discrete data utilizing different fitting functions at different intervals.…”