In the last several sections, we introduced methods that either track object boundary or propagate user labels throughout the input image. An object can be extracted out by a looped contour or with the same label. In this section, we examine two post-processing techniques to improve the accuracy of segmentation results.
One post-processing technique is to merge a small isolated sub-region to its surrounding sub-region as proposed in [103]. For example, as shown in Fig. 3.25, region A is a small region without a label, it can be merged into its surrounding region by this post-processing technique. On the other hand, in order to segment this small region out, a user should assign a label to this region explicitly.
For more accurate segmentation of the object boundary, we can develop a pixelbased refinement scheme along the boundary [4, 5]. In Lazy Snapping, Li et al. [5] represented an object boundary using triangles and allowed users to edit the boundary by dragging and moving boundary points. It is helpful to get better boundary locations with user editing.
For complex object boundaries such as hairy, furry, motion blurred, and transparent boundaries, it is difficult to get a satisfactory hard-segmentation result even with user editing. Instead, it is often to apply the alpha matting technique as a postprocessing step to refine the object boundary in this case. The goal of alpha matting is to calculate a soft segmentation to separate the foreground and background as accurately as possible. Since the object in a physical scene may have a finer spatial resolution than the size of a discretized image pixel, one pixel may contain a mix of both the foreground and background information [107].
The soft segmentation can be represented in the form of:
where I(x, y) is the observed image value at pixel (x, y), F(x, y) are B(x, y) are the foreground and background values at (x, y), and 0 ≤ α(x, y) ≤ 1 is the alpha matte function. This model was first proposed in [108] for the purpose of anti-aliasing in image segmentation. Each pixel along the object boundary is the blending result of foreground and background colors on the boundary, and the alpha value controls the weight of the foreground color.
When we calculate Eq. (3.66) in the color space, there are 7 unknowns (namely, colors of F(x, y) and B(x, y) and the alpha value α(x, y)) to be determined with only known value I(x, y) at each pixel location. Thus, the problem is ill-posed. Many regularization schemes have been proposed for Eq. (3.66) by setting constraints on F, B and α [13, 107, 109, 110]. Generally speaking, the constraints on F(x, y), B(x, y) are based on the assumption that F(x, y) and B(x, y) are smooth functions.
A couple of matting models have been proposed such as the Poisson matting, Bayes matting, RW matting, closed-form matting, robust matting, etc. Sometimes, user input is required to identify foreground, background, and transitional regions, which are referred to as the trimap [13]. In the current context, a trimap can be generated automatically from the segmentation step by extracting the object boundary bound [103]. The Soft Scissor (SS) [111] offers a real-time interactive matting tool, and it is implemented as Digital Film Tools PowerMask (http://www.digitalfilmtools. com/powermask/) with a user input similiar to that of edge-based Intelligent Scissors [41].
Another efficient boundary refinement technique is to apply an active contour method with an additional constraint [112] that is used to determine a global optimal object boundary. It aims to locate the most likely object boundary by considering both the boundary and the regional information. For segmentation methods with a hard segmentation result, a probability map based on the GMM models of the foreground and background colors is first constructed. Then, the constrained active contour technique is adopted to find the optimal boundary location. As shown in [112], this technique is effective in improving randow-walk methods [6] and the geodesic segmentation method [13] by generating an improved hard segmentation result.
To conclude, boundary editing and isolated region merging offer two postprocessing solutions in image segmentation with explicit control. The alpha matting technique is particularly efficient in handling hairy and furry complex boundaries.