Superpixel Generation by Agglomerative Clustering With Quadratic Error Minimization

Abstract

Superpixel segmentation is a popular image pre‐processing technique in many computer vision applications. In this paper, we present a novel superpixel generation algorithm by agglomerative clustering with quadratic error minimization. We use a quadratic error metric (QEM) to measure the difference of spatial compactness and colour homogeneity between superpixels. Based on the quadratic function, we propose a bottom‐up greedy clustering algorithm to obtain higher quality superpixel segmentation. There are two steps in our algorithm: merging and swapping. First, we calculate the merging cost of two superpixels and iteratively merge the pair with the minimum cost until the termination condition is satisfied. Then, we optimize the boundary of superpixels by swapping pixels according to their swapping cost to improve the compactness. Due to the quadratic nature of the energy function, each of these atomic operations has only O(1) time complexity. We compare the new method with other state‐of‐the‐art superpixel generation algorithms on two datasets, and our algorithm demonstrates superior performance.

Merge-Swap Optimization Framework for Supervoxel Generation from Three-Dimensional Point Clouds

“…Many superpixel approaches have been proposed in recent years [10][11][12] . Stutz et al [13] presented a comprehensive evaluation of 28 state-of-the-art superpixel algorithms, and some of them were designed for or can be extended to processing RGB-D images [11,[14][15][16][17][18]. With given depth information, an RGB-D image can be viewed as a 3D point set with given neighboring relationships in the camera coordinate system.…”

“…All these existing superpixel methods heavily rely on the regular structure of pixels and cannot be directly applied to supervoxel segmentation of unorganized 3D point clouds. The proposed merge-swap framework for supervoxel generation was inspired by the optimization technique proposed by [20], which was used to efficiently build superpixels by [11,21]. Equipped with a tailored energy function for supervoxels and adapted merging and swapping operations for point clouds, the proposed method generates compact supervoxels that adhere well to object boundaries.…”

“…By substituting Equations (10) and (11) into Equation 9, we obtain the energy value for the new supervoxel S i . Note that ε(S i ) can be calculated in O(1) time using our method without traversing all the points in S i .…”