A new fast DCT-based algorithm for accurate image arbitrary scaling and rotation is described. The algorithm is free from boundary effects characteristic for FFT-based algorithm and ensures perfect interpolation with no interpolation errors. The algorithm is compared with other available algorithms in terms of the interpolation accuracy, computational complexity and suitability for real time applications.
Image scaling is a frequent operation in video processing for optical metrology. In the paper, results of comparative
study of computational complexity of different algorithms for scaling digital images with arbitrary scaling factors are
presented and discussed. The following algorithms were compared: different types of spatial domain processing
algorithms (linear, cubic, cubic spline interpolation) and a new DCT-based algorithm, which implements perfect
(interpolation error free) scaling through discrete sinc-interpolation and is virtually free of boundary effects
(characteristic for the DFT-based scaling algorithms). The comparison results enable evaluation of the feasibility of realtime
implementation of the algorithms for arbitrary image scaling.
A new DCT-based algorithm for signal and image scaling by arbitrary factor is presented. The algorithm is virtually free of boundary effects and implements the discrete sinc-interpolation, which preserves the spectral content of the signal, and therefore is free from interpolation errors. Being implemented through the fast FFT-type DCT algorithm, the scaling algorithm has computational complexity of O(log[σN]) operations per output sample, where N and [σN] are number of signal input and output samples, correspondingly.
A new universal low computational complexity algorithm for numerical reconstruction of holograms recorded in near
diffraction zone is presented. The algorithm implements digital convolution in DCT domain, which makes it virtually
insensitive to boundary effects. It can be used for reconstruction of holograms for arbitrary ratios of hologram size to the
object-to-hologram distance and wavelength to camera pitch and allows image reconstruction in arbitrary scale.
Results of comparative study of the computational complexity of different algorithms for numerical reconstruction of
electronically recorded holograms are presented and discussed. The following algorithms were compared: different types
of Fourier and convolutional algorithms and a new universal DCT-based algorithm, in terms of the number of operations.
Based on the comparison results, the feasibility of real-time implementation of numerical reconstruction of holograms is
Proc. SPIE. 7724, Real-Time Image and Video Processing 2010
KEYWORDS: Diffraction, Holograms, Digital signal processing, 3D image reconstruction, Digital holography, Detection and tracking algorithms, Image processing, Fourier transforms, Convolution, Reconstruction algorithms
Convolution and correlation are very basic image processing operations with numerous applications ranging from image
restoration to target detection to image resampling and geometrical transformation. In real time applications, the crucial
issue is the processing speed, which implies mandatory use of algorithms with the lowest possible computational
complexity. Fast image convolution and correlation with large convolution kernels are traditionally carried out in the
domain of Discrete Fourier Transform computed using Fast Fourier Transform algorithms. However standard DFT based
convolution implements cyclic convolution rather than linear one and, because of this, suffers from heavy boundary
effects. We introduce a fast DCT based convolution algorithm, which is virtually free of boundary effects of the cyclic
convolution. We show that this algorithm have the same or even lower computational complexity as DFT-based
algorithm and demonstrate its advantages in application examples of image arbitrary translation and scaling with perfect
discrete sinc-interpolation and for image scaled reconstruction from holograms digitally recorded in near and far
diffraction zones. In geometrical resampling the scaling by arbitrary factor is implemented using the DFT domain scaling
algorithm and DCT-based convolution. In scaled hologram reconstruction in far diffraction zones the Fourier
reconstruction method with simultaneous scaling is implemented using DCT-based convolution. In scaled hologram
reconstruction in near diffraction zones the convolutional reconstruction algorithm is implemented by the DCT-based
Computing image local statistics is required in many image processing applications such as local adaptive image
restoration, enhancement, segmentation, target location and tracking, to name a few. These computations must be carried
out in sliding window of a certain shape and weights. Generally, it is a time consuming operation with per-pixel
computational complexity of the order of the window size, which hampers real-time applications. For acceleration of
computations, recursive computational algorithms are used. However, such algorithms are available only for windows of
certain specific forms, such as rectangle and octagon, with uniform weights. We present a general framework of fast
parallel and recursive computation of image local statistics in sliding window of almost arbitrary shape and weights with
"per-pixel" computational complexity that is substantially of lower order than the window size. As an illustration of this
framework, we describe methods for computing image local moments such as local mean and variance, image local
histograms and local order statistics (in particular, minimum, maximum, median), image local ranks, image local DFT,
DCT, DcST spectra in polygon-shaped windows as well as in windows with non-uniform weights, such as Sine lobe,
Hann, Hamming and Blackman windows.