Figure 5 - uploaded by Lucas J Van Vliet
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Image of a camera test chart with bar patterns of increasing frequency. The output images (a) and (c) have a four times higher sampling rate in both directions using MTS (σ = 1) and LSP (n = 3 samples) with 25 frames. All images are contrast stretched.
Source publication
We present various methods to increase the spatial resolution of an undersampled, and thus aliased, image sequence. The sequence is acquired by an infrared camera, which severely undersamples the image of a static scene. Vibration of the setup causes a random, sub-pixel, global translation of the scene before sampling. Although a single frame is ha...
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Discretization schemes commonly used for total variation regularization lead to images that are difficult to interpolate, which is a real issue for applications requiring subpixel accuracy and aliasing control. In the present work, we reconciliate total variation with Shannon interpolation and study a Fourier-based estimate that behaves much better...
Citations
... In this method, the minimum least-squares solution has to be obtained to find the linear Fourier phase relationship between two images. Hendriks et al. 14 compare different methods using cross correlation and a Taylor series. In this paper, we utilize a correlation method without solving the minimum least-squares problem to explore the translational differences (shifts in the x and y domains) of Fourier transforms of two images to estimate subpixel shifts between two low-resolution aliased images. ...
We present a superresolution image reconstruction from a sequence of aliased imagery. The subpixel shifts (displacement) among the images are unknown due to the uncontrolled natural jitter of the imager. A correlation method is utilized to estimate subpixel shifts between each low-resolution aliased image with respect to a reference image. An error-energy reduction algorithm is derived to reconstruct the high-resolution alias-free output image. The main feature of this proposed error-energy reduction algorithm is that we treat the spatial samples from low-resolution images that possess unknown and irregular (uncontrolled) subpixel shifts as a set of constraints to populate an oversampled (sampled above the desired output bandwidth) processing array. The estimated subpixel locations of these samples and their values constitute a spatial domain constraint. Furthermore, the bandwidth of the alias-free image (or the sensor imposed bandwidth) is the criterion used as a spatial frequency domain constraint on the oversampled processing array. The results of testing the proposed algorithm on the simulated low-resolution forward-looking infrared (FLIR) images, real-world FLIR images, and visible images are provided. A comparison of the proposed algorithm with a standard interpolation algorithm for processing the simulated low-resolution FLIR images is also provided.
... Hence, if we a priori know the correlation dependence for realization of d i , the restored signal value at the point (x i + ε) is (4) RESTORING MISSED SAMPLES In practice, it is quite often for a sample to be "missed" in the analyzed one dimensional sequence of the samples d i , obtained with the constant sampling interval, which results from some problems in the transmission channel or the recording device. Corre lation dependencies are generally not known a priori in such cases. ...
... (2) Interpolating samples of the oversampled image by the neighboring samples of the initial images: In most cases, the problem can be solved even if the num ber of initial images is less than k. For a brief review and comparison of various interpolation methods, see [4]. For fresher data and an original interpolation method that minimizes the energy of the spectrum "tails" of the restored image, see [5]. ...
Optimal linear prediction (OLP) as applied to form oversampled signals from undersampled signals is considered. The OLP-based
algorithm for aliasing suppression and sampling frequency enhancement of an image that accumulates a series of geometrically
distorted undersampled images is proposed. Results of numerical experiments showing the significant quality improvement for
images constructed by OLP are given.
Keywordsundersampled signals-aliasing-sampling frequency enhancement-image series-optimal linear prediction
... Hardie et al. [1] present an algorithm that computes the gradient of images acquired at different temporal intervals and makes a weighted interpolation between spatially adjacent pixels. In [2], C.L. Luengo Hendriks and L.J. van Vliet propose a lowcomputation method that achieves good real-time results from a sub-sampled video sequence affected by aliasing noise. Probabilistic methods are also considered. ...
... spatial variance. In(2), Iˆ is the average signal amplitude in the surrounding of the kernel center, ( ) ...
Super-resolution is a key task when browsing huge image databases over the Web; in fact, it allows for significant improvements of the service interactivity by increasing the image spatial resolution so that only thumbnail version of the images can be sent over the network. In the proposed work, the low-resolution image is first analyzed to identify several features that are significant for visual rendering and scene understanding. Such a classification is based on local frequency composition: uniform regions, edges and textures. The identified regions are then treated differently depending on the relative visual significance. Each region is further analyzed and a different interpolation approach is adopted, ranging from plain linear interpolation for homogeneous areas to edge area analysis and selective anisotropic interpolation. The combination of image region classification and adaptive-anisotropic interpolation is the main novelty of the proposed approach, which proved to outperform alternative techniques.
... Berman et al. (1994) took account of aliasing by empirically modelling the effect on phase differences. Kaltenbacher and Hardie (1996) and Luengo Hendriks and van Vliet (2000) estimated sub-pixel translations by approximating one image by a first-order Taylor series expansion of a second image. ...
... One special case is where the shifted images are sampled from a common process, for example where movement of a camera provides sub-pixel shifted frames. Several methods have been proposed (Borman and Stevenson, 1998;Luengo Hendriks and van Vliet, 2000), which can be used to increase the resolution of camera images. Another special case is digital colour imaging, where a colour mosaic filter is used to obtain red, green and blue bands, the misalignment between bands is known, but there is still a need to correct for it by interpolation, and an opportunity to use the information from the other colour bands. ...
A method is proposed for both estimating and correcting a translational mis-alignment between digital images, taking account of aliasing of high-frequency information. A parametric model is proposed for the power- and cross-spectra of the multivariate stochastic process that is assumed to have generated a continuous-space version of the images. Parameters, including those that specify misalignment, are estimated by numerical maximum likelihood. The effectiveness of the interpolant is confirmed by simulation and illustrated using multi-band Landsat images.
... It may be trivial to register systems with precisely controlled phase shifting. Popular methods for subpixel image registration include phase or cross-correlation registration 6,7 and gradient-based registration. 8,9 Image reconstruction is the process of estimating image value at arbitrary locations on a spatial continuum from a set of discrete samples. ...
Two computationally efficient methods for superresolution reconstruction and restoration of microscanning imaging systems are presented. Microscanning creates multiple low-resolution images with slightly different sample-scene phase shifts. The digital processing methods developed here combine the low-resolution images to produce an image with higher pixel resolution (i.e., superresolution) and higher fidelity. The methods implement reconstruction to increase resolution and restoration to improve fidelity in one-pass convolution with a small kernel. One method uses a small-kernel Wiener filter and the other method uses a parametric cubic convolution filter. Both methods are based on an end-to-end, continuous-discrete-continuous microscanning imaging system model. Because the filters are constrained to small spatial kernels they can be efficiently applied by convolution and are amenable to adaptive processing and to parallel processing. Experimental results with simulated imaging and with real microscanned images indicate that the small-kernel methods efficiently and effectively increase resolution and fidelity.
... If we assume ideal sampling by the optical system, then the spatial domain formulation reduces essentially to projection on a HR grid and interpolation of non-uniformly spaced samples (provided motion estimation has already been done). A comparison of HR reconstrucion results with different interpolation techniques can be found in [6] and [7]. Several techniques are given: nearest-neighbor, weighted average, least-squares plane fitting, normalized convolution using a Gaussian kernel, Papoulis-Gerchberg algorithm, and iterative reconstruction. ...
... The greater the desired magnification factor, the finer the displacements that need to be differentiated (the two are inversely proportional). 6. The presence of noise. ...
... 6 as the basis for the construction of the camera-motion vector N 16 and margin 3. where h PSF,k n 1 , n 2 ; m 1 , m 2 is the space-variant PSF and o 1 , o 2 are high-resolution coordinates for which h PSF,k n 1 , n 2 ; m 1 , m 2 is not zero. In addition to the principal constraint set Eq. 16 a second projection was used to bound the estimated pixel gray levels in the range 0,1: (19) To compensate for oversampled and undersampled regions due to vertical field displacements, a smoothing operation is performed by an additional simple projection that bandlimits the signal 25 : ...
... 15,17 Here the differential method was chosen since it produces high-accuracy results with low computational cost. The general method applied was described by Horn and Schunck 18 and implemented as an iterative procedure 19 adequate for large displacements. The method is based on minimizing the squared error of the Taylor's series expansion of the difference between the captured odd and even fields. ...
... Since this method is sensitive to noise, a prior step of field smoothing is performed with a Gaussian low-pass filter. 19 The first-order horizontal and vertical derivative operators used were h x 1 1 and h y 1 1 T , respectively. Detailed considerations for choosing these operators are presented by Elad et al. 20 Constructing the camera-motion vectors is based on the FDVs estimated above, when Eqs. 8 and 9 are used, rearranged to form the following recursion equations: ...
Staggered time delay and integration (TDI) scanning image acquisition systems are usually employed in low signal-to-noise situations such as thermal imaging. Analysis and restoration of images acquired by thermal staggered TDI sensors in the presence of mechanical vibrations that may cause space-variant image distortions (severe geometric warps and blur) are studied. The relative motion at each location in the degraded image is identified from the image when a differential technique is used. This information is then used to reconstruct the image by a technique of projection onto convex sets. The main novelty is the implementation of such methods to scanned images (columnwise). Restorations are performed with simulated and real mechanically degraded thermal images.
... If we assume ideal sampling by the optical system, then the spatial domain formulation reduces essentially to projection on a HR grid and interpolation of non-uniformly spaced samples (provided motion estimation has already been done). A comparison of HR reconstrucion results with different interpolation techniques can be found in [6] and [7]. Several techniques are given: nearest-neighbor, weighted average, least-squares plane fitting, normalized convolution using a Gaussian kernel, Papoulis-Gerchberg algorithm, and iterative reconstruction. ...
... The greater the desired magnification factor, the finer the displacements that need to be differentiated (the two are inversely proportional). 6. The presence of noise. ...
The theoretical study of micron-scale quantum-mechanical systems generally begins with two assumptions about the potential: that there is no background potential, and that any confining potential is hard-walled. In this thesis, we will look at a phenomenon that is seen when these assumptions are not made, in the context of electron conductance through two-dimensional electron gasses (2DEGs).
... In this section we want to examine how much image enhancement we can gain applying super-resolution at all and with our low complexity approach in particular. It was reported in several articles that even with the most sophisticated SR techniques the maximal resolution enhancement reaches the factor 4 [81]. Moreover, in latest publications the reachable resolution one can achieve was identified with 1.6 [75]. ...
High resolution methods have developed in the many decades. Purpose is to be obtained high resolution images. Overcome constrain of digital camera. From a set of low resolution, under-sampled, shifted, rotated and aliased images, a high resolution image is reconstructed. One of the images of the scene is a reference image. Taking advantage of aliasing-free part of the frequency domain in the images is used to calculate sub-pixel shift, angle rotate. Using the Papouis-Gerchberg algorithm to reconstruct high resolution image, which are known the relative image positions, from a set of low resolution image. The image results were archived with almost free-aliasing and good visual results.
