Conference Paper

Shape description using phase-preserving Fourier descriptor

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... Invariance of the FDs under translation is usually obtained by discarding the DC component (zeroth coefficient), since this is the only coefficient affected by translation. The scale invariance is achieved by dividing the FCs with the magnitude of the first harmonic [7], [8], [11], [12], or the sum of magnitudes of all harmonics [13], [14]. In order to obtain an invariance under rotation and starting point change, many authors discard the phase of the FCs and use only the magnitude of the FCs [7]- [9], [11], [13]. ...
... Due to this simplistic approach, valuable information about the shape is inevitably lost. Thus, two completely different shapes can have the same magnitude of FCs [14]. The phase of the FCs can be preserved and used for shape description only if the resulting descriptors are invariant to rotation and starting point change. ...
... In this paper, we will compare and discuss the following state-of-the-art methods: the cross-correlation [15], the point of maximal radius [16], the axis of least inertia (moments) [17], the phase of the first harmonic [18], the Procrustes distance [19], [20] and the pseudomirror points [14], [21]. All mentioned methods are based either on aligning shapes during the matching, or determining a nominal shape orientation prior to the matching. ...
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The magnitude-based Fourier descriptors (FD) are frequently used in shape-based image retrieval, due to their efficiency and effectiveness. Unlike the phase-preserving Fourier descriptors, the magnitude-based Fourier descriptors are inherently invariant under rotation and starting point change, but they discard all valuable information contained in the phase of the Fourier coefficients (FCs). In order to preserve the coefficients’ phase, the orientation and starting point of the shape must be determined. In this paper, we conducted a comprehensive evaluation of different state-of-the-art methods for determining nominal shape orientation, which can be used to extract phase-preserving Fourier descriptors: the point of maximal radius, the axis of least inertia (moments), the phase of the first harmonic, the cross-correlation, the Procrustes distance and the pseudomirror points. The methods were compared in terms of sensitivity to non-rigid transformations, retrieval performance, computational complexity and computational time. The experimental results give insight into the pros and cons of all analyzed methods.
... In addition, it is quite suitable for online shape retrieval because FDs has the merits of the computational efficiency and compactness. Fourier descriptors are global shape description methods which are acquired by adopting the Fourier transform over a shape signature [22,23]. Some shape signatures have been presented to obtain FDs in the literature [21][22][23][24][25][26][27]. ...
... Fourier descriptors are global shape description methods which are acquired by adopting the Fourier transform over a shape signature [22,23]. Some shape signatures have been presented to obtain FDs in the literature [21][22][23][24][25][26][27]. The strength of global shape descriptors is usually stable for the appropriate amount of distortion and noise. ...
... Finally, they employed this method for road sign recognition. Sokic et al. [23] proposed a new method to obtain the FDs, which conserve the phase information of Fourier coefficients. In their method, they introduced some specific points named pseudomirror points which is served as the reference direction of a shape. ...
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... A quick way to synthesise and analyse them with methods like Fourier descriptors (FDs) is missing, because these normally require complete contours [19], [20], with few exceptions and loss of performance [21]. An easy utilization would be very useful because FDs or similar methods [22] are extensively researched and used for active contours [23], shape description [24], shape matching [25] or identification [26]. There is work on contour completion [27], [28], but it should be even more effective not to let the problem arise and to use another post-processing method instead of the NMS. ...
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