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3-D shape of Spherical Harmonic basis functions 

3-D shape of Spherical Harmonic basis functions 

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Conference Paper
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In medical imaging research fields, three-dimensional (3D) shape modeling and analysis of anatomic structures with fewer parameters is one of important issues, which can be used for computer assisted diagnosis, surgery simulation, visualization and many medical applications. The 3-D object shape or surface can be expressed by spherical harmonics. I...

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Context 1
... Spherical Harmonics Y l represents the distance from the origin to surface point, each basis function represent individual shape illustrated in Figure 2. Spherical Harmonic basis functions are orthogonal functions and have following ...

Citations

Article
Medical image analysis plays an essential role in the diagnosis, management, and treatment of various diseases. Today, due to the capacity for fast and accurate access to high-quality images of the anatomical structures using modern medical imaging scanners, the opportunity to study and assess the shape with a wide range of medical applications is provided. One of the efficient and conscientious representation techniques to model and analyze the shape data is Fourier-based descriptors. Different studies addressed these descriptors with various clinical applications and contributed a lot in this area. This review gives a comprehensive overview of the theories and methodologies of the Fourier descriptors approaches involving 2D contours and 3D surfaces for shape modeling and analysis. This article collected studies that have employed Fourier-based descriptors in different organs with a wide range of clinical applications and placed them in five different groups, including “Segmentation,” “Classification,” “Modeling,” “Shape analysis,” and “others” from 1994 to 2021. To clarify several aspects of the research, we have summarized both the opportunities and challenges of the considered studies. In addition, we have introduced three novel subject evaluation metrics to analyze the influence and concentration of the collected studies on these five various topics. These metrics suggest a new insight into different researches usage and impact, which can be extended simply to the other works. This review is recommended for researchers working in various fields of medical image analysis using shapes containing two-dimensional contours and three-dimensional surfaces.
Article
This paper presents a novel spherical harmonics transform based 3D local feature extraction method and its application in 3D ear recognition. At first, the scale of the 3D model is normalized and the 3D points are resampled. Then the centers of local spheres are localized through grid dividing. Finally, the local spherical harmonics features are extracted and they are used for 3D ear recognition. Compared with global spherical harmonics feature, our proposed local spherical harmonics feature is more robust to pose variation and can describe the 3D model more efficiently. Extensive experimental results have testified the effectiveness of the proposed method.
Conference Paper
In this paper, we use a new method, which based on the spherical harmonics transform, to extract 3D ear rotation invariant feature from 3D ear data. And a 3D ear recognition system was built through matching ear spherical harmonics feature, which is rotation invariant in mathematical theory. Utilizing its rotation invariant property, the 3D ear recognition method could be strongly robust in pose variation. A Rank-1 recognition rate, achieved in experiment, is 96.4% on a data set of 415 subjects, and processing time also has been reduced, comparing to the well-known ICP algorithm.