The two-dimensional (2D) discrete Fourier transform (DFT) in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT) algorithm based on the vector radix (VR) 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.
To correct an over-exposure within an image, the over-exposed region (OER) must first be detected. Detecting the OER accurately has a significant effect on the performance of the over-exposure correction. However, the results of conventional OER detection methods, which generally use the brightness and color information of each pixel, often deviate from the actual OER perceived by the human eye. To overcome this problem, in this paper, we propose a novel method for detecting the perceived OER more accurately. Based on the observation that recognizing the OER in an image is dependent on the saturation sensitivity of the human visual system (HVS), we detect the OER by thresholding the saturation value of each pixel. Here, a function of the proposed method, which is designed based on the results of a subjective evaluation on the saturation sensitivity of the HVS, adaptively determines the saturation threshold value using the color and the perceived brightness of each pixel. Experimental results demonstrate that the proposed method accurately detects the perceived OER, and furthermore, the over-exposure correction can be improved by adopting the proposed OER detection method.
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