Mathematical model for shape description in DCT domain
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Mathematical model for shape description in DCT domain Ziyin Huang 1 & Bingo Wing-Kuen Ling 1 Received: 31 August 2019 / Revised: 16 June 2020 / Accepted: 28 July 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
This paper derives a mathematical relationship between the shape information of an object and their discrete cosine transform (DCT) coefficients. Here, each column of the object is put into a matrix. As the lengths of different columns in the object are different, the lengths of the columns of the matrix are reset to the maximum value among these lengths of the columns of the object and the rest elements in the columns of the matrix are set to zero. The mathematical relationship between the shape information of the object and the DCT coefficients is derived. By substituting the DCT coefficients in the derived model, the shape of the object can be obtained directly in the DCT domain. Since most of the images are coded in the DCT domain, the derived result can significantly improve the efficiency for identifying the objects. Keywords Mathematical model . Shape description . DCT domain
1 Introduction In the era of the big data, many applications such as the image retrieval applications are developed using the image databases. As a result, an efficient image description plays a very important role in our daily life. On the other hand, any scene can be considered as a collection of the individual objects. The objects can be identified by their shapes. Therefore, the most important low level feature for performing the image description is the shape information of the objects.
* Bingo Wing-Kuen Ling [email protected] Ziyin Huang [email protected]
1
School of Information Engineering, Guangdong University of Technology, No. 100, Waihuan Xi Road, Guangzhou Higher Education Mega Center, Panyu District, Guangzhou 510006 Guangdong Province, China
Multimedia Tools and Applications
It is worth noting that the edge description only takes the pixels on the edge of the object for performing the image description. One of the common edge descriptions is the Fourier description [9]. The Fourier description is to describe the edge of an object via computing the discrete Fourier transform of a complex valued vector. Here, the real part and the imaginary part of the complex valued vector are the x-coordinates and the y-coordinates of the edge points of the object, respectively [6, 11]. As the Fourier description characterizes the edge of the object in the frequency domain, the Fourier description cannot be directly used for performing the edge description in other domains such as the DCT domain. This is because the relationships between the discrete Fourier transform coefficients and the coefficients in other domains are too complicated to be exploited efficiently in real time. Moreover, as the Fourier description is a kind of the edge descriptions, the content information of the object is lost. On the other hand, the shape description takes the whole object for performing the i
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