Rectification-conducted adaptive snake for segmenting complex-boundary objects from textured backgrounds

Abstract

In this paper, an improved contour-fitting adaptive snake, namely a rectification-conducted adaptive snake (RCA-snake) is proposed for segmenting complex-boundary objects from the textured background. Based on the snaxels’ initialization, the RCA-snake comprises two steps. Initially, edge-conducted evolution (ECE) is employed for adaptations of model coefficients that accommodate ECE itself to the characteristics of salient edges for enhancing curve fitting in tracking. Following ECE, direction-induced rectification evolution corrects the boundary-unmatched snake fragments by handling the initializations of their snake-force direction and tensile-force weighting. The two steps of the RCA-snake are coordinated to enhance control of the snake model for segmenting an object with high-curvature boundaries. Simulation results demonstrate that better object-boundary coincidence can be obtained via the RCA-snake than other snake models, such as the gradient vector flow (GVF) and improved GVF, e.g., NGVF, in segmenting a complex-boundary object from textured-background images.

Appendices

Appendix 1: Dominant parameters decision

To ensure stable performance, factors such as model parameters and thresholds utilized in the RCA-snake should be classified for various image characteristics in the initial user-defined region (e.g., hand-marked rectangular area). Without searching for additional image-classification features to map such factors, the maximal gradient magnitudes (MGMs) of the line-representative pixels (LRPs) and backup LRPs resulting from the outcomes of steps 1–2 in the boundary-point detecting-sifting (BPDS) [13] can herein be reused. The MGMs with pixel values exceeding the average pixel value of all MGMs could be defined as qualified MGMs collected for further exploitation. The mean and the standard deviation of the collected MGMs are mutually normalized and then bound together as an image-characteristic vector denoted as $(m_{MGM}, \sigma _{MGM})$. An image sent for object segmentation will be classified by mapping its $(m_{MGM}, \sigma _{MGM})$ to the nearest image-characteristic vector in the trained codebook via vector quantization. Thus, an image-characteristic vector can map a set of suitable dominant factors such as $\alpha _{ECE}$(0)’s and $\beta _{ECE}$(0)’s in (12) and (13), respectively, where $\beta _{ECE}$(0) expresses the initial rigidity parameter values for ECE for one kind of clustered images. Through diverse training for the collected images featuring various attributes, the corresponding codebook shown in Table 2 can be built.

Table 2 Codebook of initial elasticity and rigidity parameters trained for ECE

A noticeable problem in applying a snake is that there are snaxels tenaciously sunk inside the object no matter how powerful the rectification method is. By categorizing the values of used thresholds as in Table 2, the occurrence probability of the aforementioned shortcoming can be decreased to a certain extent.

Appendix 2: Hadamard transform (HT)

The 2-D Hadamard transform (HT) [14] is performed on each antithetic block to obtain the horizontal, vertical, and wide-diagonal normalized energies, which can be respectively computed by

$$\begin{aligned} \left\{ {\begin{array}{l} \sum \limits _{u=1}^3 {\left| {C_{u,0} } \right| } /C_A \\ \sum \limits _{v=1}^3 {\left| {C_{0,v} } \right| } /C_A \\ \sum \limits _{v=u=1}^3 {\left| {C_{0u,v} } \right| } /C_A \\ \end{array}} \right. , \end{aligned}$$

where $C_{u,v}$ is the HT-coefficient at position $(u, v)$ and the normalized term

$$\begin{aligned} C_A =\sum \limits _{v=0}^V {\sum \limits _{u=0}^U {C_{u,v} } } . \end{aligned}$$