Active contour model (ACM) is a powerful segmentation method based on differential equation. This paper proposes a novel adaptive ACM to segment those intensity inhomogeneity images. Firstly, a novel signed pressure force function is presented with Legendre polynomials to control curve contraction. Legendre polynomials can approximate regional intensities corresponding to evolving curve. Secondly, global term of our model characterizes difference of Legendre coefficients, and local energy term characterizes fitting evolution curve of interested region. Final contour evolution will minimize the energy function. Thirdly, a correction term is employed to improve the performance of curve evolution according to the initial contour position, so wherever the initial contour being in the image, the object boundaries can be detected. Fourthly, our model combines the advantages of two classical models such as good topological changes and computational simplicity. The new model can classify regions with similar intensity values. Compared with traditional models, experimental results show effectiveness and efficiently of the new model.

中文翻译：

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一种新颖的基于全局能量和局部能量的勒让德多项式逼近图像分割

活动轮廓模型（ACM）是一种基于微分方程的强大分割方法。本文提出了一种新颖的自适应ACM来分割那些强度不均匀的图像。首先，利用勒让德多项式提出了一种新颖的带符号压力函数，以控制曲线的收缩。勒让德多项式可以近似对应于演化曲线的区域强度。其次，模型的全局项描述了勒让德系数的差异，局部能量项描述了感兴趣区域的拟合演化曲线。最终轮廓演变将使能量函数最小化。第三，根据初始轮廓位置采用校正项来改善曲线演化的性能，因此无论图像中的初始轮廓是什么，都可以检测出物体边界。第四，我们的模型结合了两个经典模型的优点，例如良好的拓扑变化和计算简单。新模型可以对强度值相似的区域进行分类。与传统模型相比，实验结果表明了新模型的有效性和有效性。