Describing Colors, Textures and Shapes for Content Based Image Retrieval - A Survey <s> Fourier Shape Descriptors <s> Abstract Shape is one of the primary low-level image features exploited in the newly emerged content-based image retrieval (CBIR). Many shape methods exist. Among these shape methods, Fourier descriptor (FD) is one of the most widely used shape descriptors due to its simple computation, clarity and coarse to fine description capability. FD has been applied to a variety of applications, including image retrieval application. Generally, FD can be acquired in a number of ways, however, FD acquired from different ways can have different retrieval performance. In this paper, we study shape retrieval using FD. Specifically, we study different ways of acquiring FD, the number of FD features needed for general shape description and the retrieval performance of different FD. A Java client–server retrieval framework has been developed to facilitate the study. The retrieval performance of the different FD is tested using a standard shape database and a commonly used performance measurement. <s> BIB001 </s> Describing Colors, Textures and Shapes for Content Based Image Retrieval - A Survey <s> Fourier Shape Descriptors <s> List of contributors Preface Part I. Theoretical Considerations: 1. Introduction Pete E. Lestrel 2. Introduction and overview of Fourier descriptors Pete E. Lestrel 3. Growth and form revisited Dwight W. Read 4. Methodological issues in the description of forms Paul O'Higgins 5. Phase angles, harmonic distance and the analysis of form Roger L. Kaesler Part II. Applications of Fourier Descriptors: 6. Closed-form Fourier analysis: a procedure for extraction of ecological information about foraminiferal test morphology Nancy Healy-Williams, Robert Ehrlich and William Full 7. Fourier descriptors and shape differences: studies on the upper vertebral column of the mouse David Johnson 8. Application of the Fourier method on genetic studies of dentofacial morphology Lindsay Richards, Grant Townsend and Kazutaka Kasai 9. Fourier analysis of size and shape changes in the Japanese skull Fumio Ohtsuki, Pete E. Lestrel, Teruo Uetake, Kazutaka Adachi and Kazuro Hanihara 10. Craniofacial variability in the hominoidea Burkhard Jacobshagen 11. Heuristic adequacy of Fourier descriptors: methodologic aspects and applications in morphology Vittorio Pesce Delfino, Teresa Lettini and Eligio Vacca 12. Analyzing human gait with Fourier descriptors Teruo Uetake 13. Elliptical Fourier descriptors of cell and nuclear shapes Giacomo Diaz, Corrado Cappai, Maria Dolores Setzu, Silvia Sirigu and Andrea Diana 14. Cranial base changes in shunt-treated hydrocephalics: Fourier descriptors Pete E. Lestrel and Jan A Huggare 15. A numerical and visual approach for measuring the effects of functional appliance therapy: Fourier descriptors Won Moon 16. Size and shape of the rabbit orbit: 3-D Fourier descriptors Pete E. Lestrel, Dwight W. Read and Charles Wolfe 17. From optical to computational Fourier transforms: the natural history of an investigation of the cancellous structure of bone Charles E. Oxnard 18. Epilogue: Fourier methods and shape analysis Neal Garrett Appendix Glossary Index. <s> BIB002
The Fourier shape descriptors are calculated by applying Fourier Transform on 1D shape signatures discussed previously which are usually derived from the shape's contour. For a shape signature z(u), the Fourier Transform can be calculated as The Fourier coefficients obtained a n (also called FDs) are normalized by using the DC component of the transform as Where FD1 is the DC component, and FD N are the Fourier coefficients. FDs are invariant to translation since the shape descriptors used to derive FDs are invariant to translation. Scale invariance is achieved through normalization of the Fourier co efficients and rotation invariance is achieved by considering only the magnitude values of FDs and ignoring the phase information. The FDs are widely used for shapes recognitions in various fields BIB001 BIB002 .