目的：针对传统彩色图像边缘检测方法中未充分利用图像色度信息、颜色模型间非线性转换过程中时间和空间的大量耗费、算法实现复杂等问题，本文将四元数引入最小核值相似区（Smallest Univalue Segment Assimilating Nucleus, SUSAN）算法中，提出一种RGB空间下的结合四元数与最小核值相似区的边缘检测算法。方法：该算法首先对彩色图像进行四元数描述，然后用改进的SUSAN算子进行边缘检测。针对其中单一几何阈值 的限制，以及检测出的边缘较粗等问题，本文采用Otsu算法自适应获取双几何阈值，再对弱边缘点集进行边缘生长，最后根据USAN重心及其对称最长轴来确定边缘局部方向，实现对边缘点的局部非极大值抑制，得到最终细化后的边缘图像。结果：实验选取一幅合成彩色图像及三幅标准图像库图像，与彩色Canny算法、SUSAN算法、及采用单阈值的本文算法进行对比，并采用Pratt品质因数衡量边缘定位精度。结果表明，本文算法能够检测出亮度相近的不同颜色区域之间的边缘，且提取的边缘比较连续、细致，漏检边缘较少。与公认边缘检测效果较好的彩色Canny算法相比，本文算法的品质因数提高了0.0120，耗时缩短了2.5279s。结论：本文提出了一种结合四元数与最小核值相似区的边缘检测算法，实现了四元数与SUSAN算子的有效融合。实验结果表明，该算法能够提高边缘定位精度，对弱噪声具有较好的抑制能力，适用于对实时性要求不高的低层次彩色图像处理。
The edge detection algorithm combining smallest univalue segment assimilating nucleus and quaternion
Objective: Edge detection is one of the most fundamental operations in image processing and scene analysis systems, the reason is that edges form the outline of an object. It is the procedure of detecting meaningful discontinuities of the image function, and provides an effective means for image segmentation, image fusion and pattern recognition. The gray image edge detection has been developing relatively saturated, but the color image edge detection has not received the same attention. Up to now, most of the existing color image edge detection algorithms are monochromatic-based methods, which produce superior effect than traditional gray-value methods. Both of them do not make full use of the chromatic information, while vector-valued techniques, treating the color information as color vectors in a vector space provided with a vector norm, just solve such a problem. However, the vector-valued methods have higher complexity and larger computation. A color image with three components can be represented in quaternion form as pure quaternions, which can preserve the vector features of the image pixels well. In consequence, aiming at several problems in the traditional color image edge detection methods, such as the insufficient use of chromatic information in color images, the large amount of time and space consumption in the process of nonlinear transformation between color models, the complex algorithm implementation, the edge detection algorithm combining smallest univalue segment assimilating nucleus and quaternion in RGB space was proposed. Method: For a preferable color image edge detection result, we take account of the algebraic operation and spatial characteristics about the quaternion and the simple and effective edge detection performance of the SUSAN algorithm in our method. The steps of this approach can be summarized as follows: Firstly, represent the color images with pure quaternions and normalize each pixel; Secondly, edge detect using SUSAN operator, which generates the thick edge because of the constraint of fixed geometry threshold , so the Otsu algorithm is applied to adaptively capture the double geometry thresholds; Thirdly, we make the edge growth on the weak edge set and determine the local edge direction according to the center of gravity and the longest axis of symmetry of USAN; Finally, perform the local non-maximum suppression operation to obtain the final thinned edge image. Result: In order to demonstrate the effectiveness and robustness of our method, choosing three classic color images and a synthetic color image with four blocks for specific colors, we make a comparison with other edge detection algorithms, including the color Canny algorithm, SUSAN algorithm and our method with a fixed threshold. Setting two different forms of geometric threshold in our method is to verify whether the selection of the threshold is influential to the final effect of edge image. And we use Pratt quality factor to make a quantitative evaluation of edge positioning accuracy. The experiment results show that our method with less lost edges can detect the edges of different color regions with similar brightness, and the extracted edges are continuous and meticulous. Besides, for the color images with weak noise, our method is so robust that it still can effectively detect the real edge points. Compared with the color Canny algorithm which has the preferable effect of edge detection in color images, the quality factor of our method improved by 0.0120, the operation time reduced by 2.5279s. Conclusion: In this thesis, we put forward to a the edge detection algorithm combining smallest univalue segment assimilating nucleus and quaternion, realizing the effective fusion of quaternion and SUSAN operator. Setting several different comparative experiments, both subjective evaluation and objective evaluation show that our method, effectively suppressing the weak noise and improving the accuracy of edge localization, is really suitable for low level color image processing with lower demand in real-time.