# A Two-Stage Gradient Ascent-Based Superpixel Framework for Adaptive Segmentation
## 4 Experiment and Analysis
### Visual Comparison and Quantitative Metrics  
Figure 3 provides four results for visual comparison of superpixels obtained by the above-mentioned algorithms. As is intuitively depicted, SLIC, sSLIC and LSC all present relative compact and uniform superpixel apart from watershed. Nevertheless, in order to maintain compactness, SLIC fails in some detail-rich regions such as ear of the rhinoceros and antler of the wapiti. Moreover, the biggest advantage of SLIC is the high efficiency, which may sacrifice some performance, for instance, the content awareness. Therefore, in some regions with weak boundaries, e.g., the head of the leopard, it is difficult for SLIC to attach the actual borders since it merely relies on clustering of local color-spatial features [30].  
Figure 3: \(Cont.\)Although the segmentation quality seems undesirable, watershed has two merits well suited for superpixel subdivision. One is the ability to segment patches with any shape, avoiding regular region restriction such as SLIC and LSC. The other is spatial arrangement of the resulting regions by the choice of markers mentioned in Section 3.2, which which gets rid of the constraint of spatial compactness. Therefore, if markers are set in under-segmentation regions with weak boundaries and complicated textures properly, then watershed would perform subtle local treatments and show a more accurate outline detection.  
For quantitatively evaluating the performance of boundary adherence, two commonly used evaluation metrics in superpixel segmentation methods are taken into account in this subsection. Specifically, boundary recall (BR) [29] and under-segmentation error (UE) [15] are adopted, with emphasis on edge and region consistency, respectively.  
BR measures the degree of ground truth boundaries covered by superpixel boundaries. According to [11], coverage radius is set to 1 pixel. As revealed in Figure 4a, the proposed method outperforms other three comparative methods in a wide range of superpixel size, which is in accordance with the subjective comparison in Figure 3. The superiority of the two-stage framework is owing to utilizing the idea of hierarchical partition by SLIC and Watershed. In fact, during the speeding up clustering process, sSLIC inherits and adopts local k-means method in SLIC, without considering any global constrain strategy differently than LSC (that is why the overall BR of SLIC is smaller than the latter). Besides, the compact property seems easy to degrade in complicated textures regions  
Figure 3: Visual comparison among four different methods. (**a**) Result by Watershed; (**b**) Result by SLIC Superpixel; (**c**) Result by the proposed method; (**d**) Result by Linear Spectral Clustering (LSC) Superpixel. Alternating rows show each segmented image followed by local details of each image.  
constrained by single color-spatial distance. Therefore, while resulting partitions subdivided by watershed are highly irregular in size and shape, they still perform satisfactory boundary adherence. As a result, the following two properties, regularity and perceptual satisfaction sacrifice a little for a better boundary recall.  
UE measures the ability of a group of gathered superpixels depicting the ground truth object, which indicates the representation capacity for superpixels as region-based features. The metric follows [15] and sets the tolerance to 5%. As shown in Figure 4, the proposed method outperforms the three others with the lowest UE in a wide range of superpixel density. Since SLIC holds an acceptable performance on UE, the proposed framework is able to separate almost all superpixels overlapping with parts of an object by ground truth boundaries even further. Eventually, the newly consequent outlines draw a more concrete region of the object. It is worth mentioning that, some under-segmented regions only suffer \"dichotomy\" into two sub-regions, which is proved experimentally reasonable in practice.