Adaptively quadratic (AQua) image interpolation

New Efficient Interpolation Techniques for Medical Images.. [DOI: 10.21203/rs.3.rs-2869416/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

This paper presents new efficient six image interpolation techniques that aim to obtain high resolution images from low resolution ones. The problem of dealing with image interpolation as an inverse problem was treated in wavelet domain through the first proposed approach. This approach estimates wavelet coefficients in high frequency sub-images using least squares algorithm. The approach reveals performance improvement in PSNR and MSE values compared to bilinear and least squares algorithm. A second approach based on using artificial neural network for modeling the maximum entropy interpolation algorithm was presented. Training the suggested network is achieved by adjusting its weights using learning algorithm to minimize the sum of squared error between target and actual output of output neurons. The proposed approach requires fewer computations than the conventional high-quality image interpolation methods with little reduction in PSNR compared to the maximum entropy algorithm. A third algorithm which combines new contourlet transform and edge-based interpolation algorithm was proposed to improve object boundaries regularity which could be achieved by treating each successive approximation of the high-resolution image as a noisy approximation, hence enforcing the contourlet coefficients to have a sparsity constraint. The proposed algorithm gives an improvement of 2 dB in PSNR compared to IIGR algorithm and achieves the best MSE and correlation coefficient. The fourth approach presents an efficient method to get HR images from the fusion of Magnetic resonance and computed tomography images by adopting least-squares strategy to iteratively obtain wavelet sub-bands of the target HR image. The proposed approach was found to achieve good results especially when the curvelet transform is used to merge the CT and MR images. The fifth approach presents neural modeling of the maximum entropy image interpolation algorithm based on both curvelet and wavelet fusion. Through this approach the fusion process is performed while edges with a curved nature are preserved. Results showed that applying curvelet transform in the fusion of CT and MR images is better than DWT fusion and that interpolating the fused image by neural modeling of maximum entropy image interpolation algorithm is superior to interpolating the original MR and CT images. The sixth approach presents a new image scale-up, super-resolution, approach based on image fusion principle. MR and CT images were scaled-up using sparse-representation modeling with dictionary learning algorithms of Yang et. al. and Michael et. al.. The images were fused by discrete wavelet and curvelet transforms, then scaled-up by the same algorithms. Simulation results showed that scaling-up the fused MR and CT images, either by wavelet or curvelet fusion techniques, gives higher PSNR values than scaling-up the MR and CT image separately.

Image Zooming Based on Two Classes of C1-Continuous Coons Patches Construction with Shape Parameters over Triangular Domain

Image interpolation is important in image zooming. To improve the quality of image zooming, in this work, we proposed a class of rational quadratic trigonometric Hermite functions with two shape parameters and two classes of C 1 -continuous Coons patches constructions over a triangular domain by improved side–side method and side–vertex method. Altering the values of shape parameters can adjust the interior shape of the triangular Coons patch without influencing the function values and partial derivatives of the boundaries. In order to deal with the problem of well-posedness in image zooming, we discussed symmetrical sufficient conditions for region control of shape parameters in the improved side–side method and side–vertex method. Some examples demonstrate the proposed methods are effective in surface design and digital image zooming. C 1 -continuous Coons patches constructed by the proposed methods can interpolate to scattered 3D data. By up-sampling to the constructed interpolation surface, high-resolution images can be obtained. Image zooming experiment and analysis show that compared to bilinear, bicubic, iterative curvature-based interpolation (ICBI), novel edge orientation adaptive interpolation scheme for resolution enhancement of still images (NEDI), super-resolution using iterative Wiener filter based on nonlocal means (SR-NLM) and rational ball cubic B-spline (RBC), the proposed method can improve peak signal to noise ratio (PSNR) and structural similarity index (SSIM). Edge detection using Prewitt operator shows that the proposed method can better preserve sharp edges and textures in image zooming. The proposed methods can also improve the visual effect of the image, therefore it is efficient in computation for image zooming.

A MAP-based image interpolation method via Viterbi decoding of Markov chains of interpolation functions

A new method of image resolution up-conversion (image interpolation) based on maximum a posteriori sequence estimation is proposed. Instead of making a hard decision about the value of each missing pixel, we estimate the missing pixels in groups. At each missing pixel of the high resolution (HR) image, we consider an ensemble of candidate interpolation methods (interpolation functions). The interpolation functions are interpreted as states of a Markov model. In other words, the proposed method undergoes state transitions from one missing pixel position to the next. Accordingly, the interpolation problem is translated to the problem of estimating the optimal sequence of interpolation functions corresponding to the sequence of missing HR pixel positions. We derive a parameter-free probabilistic model for this to-be-estimated sequence of interpolation functions. Then, we solve the estimation problem using a trellis representation and the Viterbi algorithm. Using directional interpolation functions and sequence estimation techniques, we classify the new algorithm as an adaptive directional interpolation using soft-decision estimation techniques. Experimental results show that the proposed algorithm yields images with higher or comparable peak signal-to-noise ratios compared with some benchmark interpolation methods in the literature while being efficient in terms of implementation and complexity considerations.

Design of interchannel MRF model for probabilistic multichannel image processing

In this paper, we present a novel framework that exploits an informative reference channel in the processing of another channel. We formulate the problem as a maximum a posteriori estimation problem considering a reference channel and develop a probabilistic model encoding the interchannel correlations based on Markov random fields. Interestingly, the proposed formulation results in an image-specific and region-specific linear filter for each site. The strength of filter response can also be controlled in order to transfer the structural information of a channel to the others. Experimental results on satellite image fusion and chrominance image interpolation with denoising show that our method provides improved subjective and objective performance compared with conventional approaches.

Nonlinear image upsampling method based on radial basis function interpolation

In this paper, we present a novel edge-directed upsampling method based on radial basis function (RBF) interpolation. In order to remove artifacts such as blurred edges or blocking effects, we suggest a nonlinear method capable of taking edge information into account. The resampling evaluation is determined according to the edge orientation. The proposed scheme is as simple to implement as linear methods but it demonstrates improved visual quality by preserving the edge features better than the classical linear interpolation methods. The algorithm is compared with some well-known linear schemes as well as recently developed nonlinear schemes. The resulting images demonstrate the new algorithm's ability to magnify an image while preserving the edge features.

On the role of exponential splines in image interpolation

A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks.

Image interpolation by adaptive 2-D autoregressive modeling and soft-decision estimation

The challenge of image interpolation is to preserve spatial details. We propose a soft-decision interpolation technique that estimates missing pixels in groups rather than one at a time. The new technique learns and adapts to varying scene structures using a 2-D piecewise autoregressive model. The model parameters are estimated in a moving window in the input low-resolution image. The pixel structure dictated by the learnt model is enforced by the soft-decision estimation process onto a block of pixels, including both observed and estimated. The result is equivalent to that of a high-order adaptive nonseparable 2-D interpolation filter. This new image interpolation approach preserves spatial coherence of interpolated images better than the existing methods, and it produces the best results so far over a wide range of scenes in both PSNR measure and subjective visual quality. Edges and textures are well preserved, and common interpolation artifacts (blurring, ringing, jaggies, zippering, etc.) are greatly reduced.

Isocube: exploiting the cubemap hardware

This paper proposes a novel six-face spherical map, isocube, that fully utilizes the cubemap hardware built in most GPUs. Unlike the cubemap, the proposed isocube uniformly samples the unit sphere (uniformly distributed), and all samples span the same solid angle (equally important). Its mapping computation contains only a small overhead. By feeding the cubemap hardware with the six-face isocube map, the isocube can exploit all built-in texturing operators tailored for the cubemap and achieve a very high frame rate. In addition, we develop an anisotropic filtering that compensates aliasing artifacts due to texture magnification. This filtering technique extends the existing hardware anisotropic filtering and can be applied not only to the proposed isocube, but also to other texture mapping applications.

Fast and stable bayesian image expansion using sparse edge priors

Smoothness assumptions in traditional image expansion cause blurring of edges and other high-frequency content that can be perceptually disturbing. Previous edge-preserving approaches are either ad hoc, statistically untenable, or computationally unattractive. We propose a new edge-driven stochastic prior image model and obtain the maximum a posteriori (MAP) estimate under this model. The MAP estimate is computationally challenging since it involves the inversion of very large matrices. An efficient algorithm is presented for expansion by dyadic factors. The technique exploits diagonalization of convolutional operators under the Fourier transform, and the sparsity of our edge prior, to speed up processing. Visual and quantitative comparison of our technique with other popular methods demonstrates its potential and promise.

Image denoising using total least squares

In this paper, we present a method for removing noise from digital images corrupted with additive, multiplicative, and mixed noise. An image patch from an ideal image is modeled as a linear combination of image patches from the noisy image. We propose to fit this model to the real-world image data in the total least square (TLS) sense, because the TLS formulation allows us to take into account the uncertainties in the measured data. We develop a method to reduce the contribution from the irrelevant image patches, which will sharpen the edges and reduce edge artifacts at the same time. Although the proposed algorithm is computationally demanding, the image quality of the output image demonstrates the effectiveness of the TLS algorithms.

Image interpolation by two-dimensional parametric cubic convolution

Cubic convolution is a popular method for image interpolation. Traditionally, the piecewise-cubic kernel has been derived in one dimension with one parameter and applied to two-dimensional (2-D) images in a separable fashion. However, images typically are statistically nonseparable, which motivates this investigation of nonseparable cubic convolution. This paper derives two new nonseparable, 2-D cubic-convolution kernels. The first kernel, with three parameters (designated 2D-3PCC), is the most general 2-D, piecewise-cubic interpolator defined on [-2, 2] x [-2, 2] with constraints for biaxial symmetry, diagonal (or 90 degrees rotational) symmetry, continuity, and smoothness. The second kernel, with five parameters (designated 2D-5PCC), relaxes the constraint of diagonal symmetry, based on the observation that many images have rotationally asymmetric statistical properties. This paper also develops a closed-form solution for determining the optimal parameter values for parametric cubic-convolution kernels with respect to ensembles of scenes characterized by autocorrelation (or power spectrum). This solution establishes a practical foundation for adaptive interpolation based on local autocorrelation estimates. Quantitative fidelity analyses and visual experiments indicate that these new methods can outperform several popular interpolation methods. An analysis of the error budgets for reconstruction error associated with blurring and aliasing illustrates that the methods improve interpolation fidelity for images with aliased components. For images with little or no aliasing, the methods yield results similar to other popular methods. Both 2D-3PCC and 2D-5PCC are low-order polynomials with small spatial support and so are easy to implement and efficient to apply.

Demosaicing using optimal recovery

Color images in single-chip digital cameras are obtained by interpolating mosaiced color samples. These samples are encoded in a single-chip charge-coupled device by sampling the light after it passes through a color filter array (CFA) that contains different color filters (i.e., red, green, and blue) placed in some pattern. The resulting sparsely sampled images of the three-color planes are interpolated to obtain the complete color image. Interpolation usually introduces color artifacts due to the phase-shifted, aliased signals introduced by the sparse sampling of the CFAs. This paper introduces a nonlinear interpolation scheme based on edge information that produces high-quality visual results. The new method is especially good at reconstructing the image around edges, a place where the visual human system is most sensitive.