# A Two-Stage Gradient Ascent-Based Superpixel Framework for Adaptive Segmentation
## 1 Introduction  
Image segmentation has been widely employed in a wide range of computer vision applications, which is essentially a process of dividing an image into several fragments without intersecting. A superpixel [1] is a homogeneity description of texture, color and other features in accordance with visual sense. As the term \"superpixel\" suggests, it meets the goal of representing an image by perceptually meaningful entitieswhich heavily reduces the number of pixels. This is why superpixels can significantly improve the efficiency of segmentation in practice and become a key preprocessing step for advanced tasks such as video segmentation [2], target tracking [3], object recognition [4], super-resolution [5] and depth estimation [6]. The existing superpixel methods can be generally divided into two categories: graph-based methods and gradient ascent methods. In a graph-based algorithm, superpixels are produced by minimizing a cost function defined over the graph in which each pixel is regarded as a node. Normalized cuts (Ncut) [7] is a representative algorithm based on contour and texture information resulting in regular and compact superpixels, however, it is poor in accuracy and computing efficiency, especially in dealing with large scale images. [PERSON] and [PERSON] [8] propose an efficient graph-based approach through the minimum spanning tree, which shows relative precise adherence to image boundaries, but the procedure is unconscious and the patches are very irregular. Compact superpixels and Constant-intensity superpixels [9], as known as GCa and GCb, are two approaches of a global optimization approach based on [10]. In those frameworks, overlapping image patches are stitched together to generate superpixels where every single pixel belongs to one of the overlapping regions. Superpixels from GCa has the property of uniform compactness with regular shape and size, while GCb performs better in boundary adherence, which shows accurate segmentation precision. However,these two methods are difficult to adjust parameters and limited in subsequent processing. Entropy Rate Superpixel (ERS) [11] maps one image to an undirected graph consisting of vertices and edges sets, so that a subset of edges is selected to form the resulting graph with directly controlled number of sub-graphs based on entropy rate. Lazy Random Walk (LRW) [12] superpixel segmentation also converts segmentation into graph partition, which iteratively optimizes superpixels by a new energy function and shows well segmentation accuracy, but the time consumption is unsatisfactory for later-stage processing. Gradient ascent methods, also called clustering-based methods, propose the idea of clustering and iteratively refine the process until it meets a pre-defined criterion. Turbopixels [13] adopts level-set based geometric flow for each seed to generate dense over-segmented and compact superpixels. It combines a curve evolution model for dilation with a skeletonization process for spatial constraint, but sometimes it provides unsatisfactory results in practice. Watershed [14] is a relatively fast segmentation approach based on the topological theory with mathematical morphology. The implementation can be described as a flooding process, it detects the minima of gradients image and pixels at the minima will be flooded. However, the amount of superpixels and their compactness is out of control. Simple Linear Iterative Clustering (SLIC) [15] utilizes local k-means clustering to partial pixels based on color and spatial distance. Compared to many state-of-the-art superpixel methods, SLIC outperforms in several desirable properties for superpixel segmentation, such as the controllability of desired number and compactness through input parameters. Linear Spectral Clustering (LSC) [16] adopts a variant of k-means method to iteratively refine uniformly sampled superpixels similar to SLIC. Whereas it applies a weighted k-means method in the transformed 10-dimensional feature space by kernel function, which further makes an improvement of Ncut [7].