Leonid P. Yaroslavsky

Convolution-based interpolation for fast, high-quality rotation of images

This paper focuses on the design of fast algorithms for rotating images and preserving high quality. The basis for the approach is a decomposition of a rotation into a sequence of one-dimensional translations. As the accuracy of these operations is critical, we introduce a general theoretical framework that addresses their design and performance. We also investigate the issue of optimality and present an improved least-square formulation of the problem. This approach leads to a separable three-pass implementation of a rotation using one-dimensional convolutions only. We provide explicit filter formulas for several continuous signal models including spline and bandlimited representations. Finally, we present rotation experiments and compare the currently standard techniques with the various versions of our algorithm. Our results indicate that the present algorithm in its higher-order versions outperforms all standard high-accuracy methods of which we are aware, both in terms of speed and quality. Its computational complexity increases linearly with the order of accuracy. The best-quality results are obtained with the sine-based algorithm, which can be implemented using simple one-dimensional FFTs.

Algorithm for reconstruction of digital holograms with adjustable magnification

A new algorithm that allows for reconstruction of digital holograms with adjustable magnification is proposed. The algorithm involves two reconstruction steps implemented by a conventional single Fourier-transform algorithm. The advantages of the algorithm lie in its adaptability to various object sizes and recording distances as well as in its capability to maintain the pitch of a reconstructed image, independent of the reconstruction distance and wavelength for objects larger than a CCD. The feasibility of the algorithm is demonstrated by experiments. The algorithm is especially useful for reconstructing color holograms and for metrological applications.

Real-time 2D to 3D video conversion

We present a real-time implementation of 2D to 3D video conversion using compressed video. In our method, compressed 2D video is analyzed by extracting motion vectors. Using the motion vector maps, depth maps are built for each frame and the frames are segmented to provide object-wise depth ordering. These data are then used to synthesize stereo pairs. 3D video synthesized in this fashion can be viewed using any stereoscopic display. In our implementation, anaglyph projection was selected as the 3D visualization method, because it is mostly suited to standard displays.

Local adaptive image restoration and enhancement with the use of DFT and DCT in a running window

On the base of local criteria of processing quality, a class of local adaptive linear filters for image restoration and enhancement is introduced. The filters work in a running window in the domain of DFT of DCT and have O (size of the window) computational complexity thanks to recursive algorithms of running DFT and DCT. The filter design and the recursive computation of running DCT are outlined and filtering for edge preserved noise suppression, blind image restoration and enhancement is demonstrated.

Efficient algorithm for discrete sinc interpolation

A new computing method for discrete-signal sinc interpolation suitable for use in image and signal processing and the synthesis of holograms is described. It is shown to be superior to the commonly used zero-padding interpolation method in terms of interpolation accuracy, flexibility, and computational complexity.

Transform domain image restoration methods: review, comparison, and interpretation

Two families of transform domain signal restoration (denoising and deblurring) and enhancement methods well suited to processing non-stationary signals are reviewed and comprehensively compared in their different modifications in terms of their signal restoration capability and computational complexity: sliding window transform domain (SWTD) filters and wavelet (WL) based algorithms. SWTD filters work in sliding window in the domain of an orthogonal transform and, in each position of the window, nonlinearly transform window transform coefficients to generate an estimate of the central pixel of the window. As a transform, DCT has been found to be one of the most efficient in most applications. WL methods act globally and apply element-wise nonlinear transformation similar to those used in SWTD methods to the wavelet transform coefficients to generate an estimate of the output signal. The paper provides results of extensive experimental comparisons of image restoration capabilities of the methods and demonstrates that they can naturally be interpreted in a unified way as different implementations of signal sub-band decomposition with uniform (in SWTD filters) or logarithmic (for WL-methods) arrangement of signal sub-bands and element-wise processing decomposed components. As a bridge, a hybrid wavelet/sliding window processing that combines advantages of both methods is described.

Is the phase-only filter and its modifications optimal in terms of the discrimination capability in pattern recognition?

We compare several recently proposed filters for pattern recognition and show that they approximate more or less the optimal filter, which, however, is not so easy to implement.

Three methods that improve the visual quality of colour anaglyphs

Anaglyphs are one of the most economical methods for three-dimensional visualization. This method, however, suffers from severe drawbacks such as loss of colour and extreme discomfort for prolonged viewing. We propose several methods for anaglyph enhancement that rely on stereo image registration, defocusing and nonlinear operations on synthesized depth maps. These enhancements substantially reduce unwanted ghosting artefacts, improve the visual quality of the images, and make comfortable viewing of the same sequence possible in three-dimensional as well as the two-dimensional mode of the same sequence.

Measurement of surface roughness by speckle correlation

Measurement of the roughness of solid surfaces by digital speckle correlation of video signals is reported. Speckle patterns appearing in the diffraction field of a laser-illuminated sample are taken by a CCD before and after the change of the incident angle or the laser wavelength, and their cross-correlation is calculated from which surface roughness can be evaluated. The theoretical cross-correlation function is first derived that describes speckle displacement and decorrelation. Its peak height is then provided as a function of the change of the incident angle or the wavelength. The decorrelation curve against speckle displacement is shown to depend on the surface roughness. The derived analytical relationships were verified by numerical simulations that used two-dimensional arrays of random numbers with various maximum values representing the maximum surface roughness. The relationship between the normal correlation calculated by the theory and the phase-only correlation adopted in the experiment was also evaluated by the simulation. In experiments various roughness standards for metal were measured by using a quick processor employing the phase-only correlation algorithm. The results were compared with those obtained from a mechanical stylus, and good agreement was observed between them for root-mean-square roughnesses between several micrometers and several tens of micrometers.

A Fourier based algorithm for tracking SPAMM tags in gated magnetic resonance cardiac images

A method is described for automatically tracking spatial modulation of magnetization tag lines on gated cardiac images. The method differs from previously reported methods in that it uses Fourier based spatial frequency and phase information to separately track horizontal and vertical tag lines. Use of global information from the frequency spectrum of an entire set of tag lines was hypothesized to result in a robust algorithm with decreased sensitivity to noise. The method was validated in several ways: first, actual tagged cardiac images at end diastole were deformed known amounts, and the algorithms predictions compared to the known deformations. Second, tagged, gated images of the thigh muscle (assumed to have similar signal to noise characteristics as cardiac images, but to not deform with time) were created. Again the algorithmic predictions could be compared to the known (zero magnitude) deformations and to thigh images which had been artificially deformed. Finally, actual cardiac tagged images were acquired, and comparisons made between manual, visual, determinations of tag line locations, and those predicted by the algorithm. At 0.5 T, the mean bias of the method was < 0.34 mm even at large deformations and at late (noisy) times. The standard deviation of the method, estimated from the tagged thigh images, was < 0.7 mm even at late times. The method may be expected to have even lower error at higher field strengths.