Showing papers on "Bicubic interpolation published in 1999"

Survey: interpolation methods in medical image processing

Abstract: Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sine; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic B-spline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1/spl times/1 up to 8/spl times/8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced and fundamental properties of interpolators are derived. Successful methods should be direct current (DC)-constant and interpolators rather than DC-inconstant or approximators. Each method's parameters are tuned with respect to those properties. This results in three novel kernels, which are introduced in this paper and proven to be within the best choices for medical image interpolation: the 6/spl times/6 Blackman-Harris windowed sinc interpolator, and the C2-continuous cubic kernels with N=6 and N=8 supporting points. For quantitative error evaluations, a set of 50 direct digital X-rays was used. They have been selected arbitrarily from clinical routine. In general, large kernel sizes were found to be superior to small interpolation masks. Except for truncated sine interpolators, all kernels with N=6 or larger sizes perform significantly better than N=2 or N=3 point methods (p/spl Lt/0.005). However, the differences within the group of large-sized kernels were not significant. Summarizing the results, the cubic 6/spl times/6 interpolator with continuous second derivatives, as defined in (24), can be recommended for most common interpolation tasks. It appears to be the fastest six-point kernel to implement computationally. It provides eminent local and Fourier properties, is easy to implement, and has only small errors. The same characteristics apply to B-spline interpolation, but the 6/spl times/6 cubic avoids the intrinsic border effects produced by the B-spline technique. However, the goal of this study was not to determine an overall best method, but to present a comprehensive catalogue of methods in a uniform terminology, to define general properties and requirements of local techniques, and to enable the reader to select that method which is optimal for his specific application in medical imaging.

Regularity-preserving image interpolation

Abstract: Assumptions about image continuity lead to oversmoothed edges in common image interpolation algorithms. A wavelet-based interpolation method that imposes no continuity constraints is introduced. The algorithm estimates the regularity of edges by measuring the decay of wavelet transform coefficients across scales and preserves the underlying regularity by extrapolating a new subband to be used in image resynthesis. The algorithm produces visibly sharper edges than traditional techniques and exhibits an average peak signal-to-noise ratio (PSNR) improvement of 2.5 dB over bilinear and bicubic techniques.

Image interpolation using neural networks

Abstract: This work presents an image interpolation method based on a multilayer perceptron. The method is tested in noise-free as well as noisy line doubling and image expansion problems. Two adaptive algorithms are compared. Results show that the proposed method improves image interpolation.

Monotonic cubic spline interpolation

Abstract: This paper describes the use of cubic splines for interpolating monotonic data sets. Interpolating cubic splines are popular for fitting data because they use low-order polynomials and have C/sup 2/ continuity, a property that permits them to satisfy a desirable smoothness constraint. Unfortunately, that same constraint often violates another desirable property: monotonicity. The goal of this work is to determine the smoothest possible curve that passes through its control points while simultaneously satisfying the monotonicity constraint. We first describe a set of conditions that form the basis of the monotonic cubic spline interpolation algorithm presented. The conditions are simplified and consolidated to yield a fast method for determining monotonicity. This result is applied within an energy minimization framework to yield linear and nonlinear optimization-based methods. We consider various energy measures for the optimization objective functions. Comparisons among the different techniques are given, and superior monotonic cubic spline interpolation results are presented.

Quantitative Comparison of Sinc-Approximating Kernels for Medical Image Interpolation

Abstract: Interpolation is required in many medical image processing operations. From sampling theory, it follows that the ideal interpolation kernel is the sinc function, which is of infinite extent. In the attempt to obtain practical and computationally efficient image processing algorithms, many sinc-approximating interpolation kernels have been devised. In this paper we present the results of a quantitative comparison of 84 different sinc-approximating kernels, with spatial extents ranging from 2 to 10 grid points in each dimension. The evaluation involves the application of geometrical transformations to medical images from different modalities (CT, MR, and PET), using the different kernels. The results show very clearly that, of all kernels with a spatial extent of 2 grid points, the linear interpolation kernel performs best. Of all kernels with an extent of 4 grid points, the cubic convolution kernel is the best (28% – 75% reduction of the errors as compared to linear interpolation). Even better results (44% – 95% reduction) are obtained with kernels of larger extent, notably the Welch, Cosine, Lanczos, and Kaiser windowed sinc kernels. In general, the truncated sinc kernel is one of the worst performing kernels.

Rotation of NMR images using the 2D chirp-z transform.

Abstract: A quick and accurate way to rotate and shift nuclear magnetic resonance (NMR) images using the two-dimensional chirp-z transform is presented. When the desired image grid is rotated and shifted from the original grid due to patient motion, the chirp-z transform can reconstruct NMR images directly onto the ultimate grid instead of reconstructing onto the original grid and then applying interpolation to get the final real-space image in the conventional way. The rotation angle and shift distances are embedded in the parameters of the chirp-z transform. The chirp-z transform implements discrete sinc interpolation to get values at grid points that are not exactly on the original grid when applying the inverse Fourier transform. Therefore, the chirp-z transform is more accurate than methods such as linear or bicubic interpolation and is more efficient than direct implementation of sinc interpolation because the sinc interpolation is implemented at the same time as reconstruction from k-space.

Image interpolation circuit architecture and method for fast bi-cubic interpolation of image information

Abstract: A circuit architecture and method are provided for interpolating a first color value associated with a first color and a second color value associated with a second color for use in generating a pixel that represents a portion of a digital image, based on a third color value that is associated with a third color. Pixel data generated by a digital image sensor is serially received at a register array organized in rows and columns that correspond to pixels of interest that are used in a bicubic interpolation process. Values stored in registers of the register array are coupled to and continuously available to four (4) dot product modules and an interpolator. As the serial data arrives, it is clocked stepwise through the registers, and concurrently used by the dot product modules and interpolator to compute the first color value and the second color value. Data that reaches the end of a line of registers is moved into a corresponding shift register for temporary storage until it is needed again. Advantageously, the method may be implemented in integrated circuit hardware and using fast combinational logic with no CPU multiply operations and no floating-point operations. A particular application is in interpolating complementary colors for pixel information received from a color area sensor, such as a CCD image sensor, in a digital camera.

A new approach to interpolating scaling functions

Abstract: We present a new method to construct interpolating refinable functions in higher dimensions. The approach is based on the solutions to specific Lagrange interpolation problems by polynomials and applies to a large class of scaling matrices. The resulting scaling functions automatically satisfy certain Strang-Fix conditions. Several examples are discussed.

Interpolation of ray theory traveltimes within ray cells

Abstract: SUMMARY 3-D ray tracing followed by interpolation of the computed quantities amongst the rays is a powerful tool for the computation of ray theory traveltimes, amplitudes and other quantities at the gridpoints of dense rectangular grids. Several methods based on the decomposition of the model volume into ray cells, and on further interpolation within the individual ray cells, have recently been introduced. We propose bilinear and bicubic interpolation schemes, which should be applicable in any modelling method based on interpolation within ray cells. The bicubic interpolation is designed for traveltimes and the bilinear interpolation for other quantities. The interpolation schemes have been incorporated into a controlled initial-value ray tracing program package. Multivalued ray theory traveltime computation in a heterogeneous 3-D model is shown as an example.

Some Remarks on Interpolation of Nonstationary Oceanographic Fields

Abstract: The performance of four methods for interpolating anisotropic, spatially nonstationary fields is examined. The methods are optimal interpolation (OI, also known as objective analysis), spline interpolation, multiquadric–biharmonic method (MQ–B), and the inverse distance weighted method. The tests were performed using multiple realizations of random bivariate fields with known underlying statistics, as well as highly anisotropic and nonhomogeneous temperature and salinity fields across the Antarctic Circumpolar Current (ACC). The results of tests using homogeneous random fields show that all methods except the inverse distance method have similar performance in the accuracy. When the interpolated field is sampled adequately and data distributions are dense, the presence of spatial deviations of the field statistics from the field average will limit the interpolation skill of OI to be gained from an increase in data density. In contrast, interpolation methods such as spline and MQ–B, which adjust t...

B-Spline Surface Approximation to Cross-Sections Using Distance Maps

Abstract: The shape reconstruction of a 3D object from its 2D crosssections is important for reproducing it by NC machining or rapid prototyping In this paper, we present a method of surface approximation to cross-sections with multiple branching problems In this method, we first decompose each multiple branching problem into a set of single branching problems by providing a set of intermediate contours using distance maps For each single branching region, a procedure then performs the skinning of contour curves represented by cubic B-spline curves on a common knot vector, each of which is fitted to its contour points within a given accuracy In order to acquire a more compact representation for the surface, the method includes an algorithm for reducing the number of knots in the common knot vector The approximation surface to the crosssections is represented by a set of bicubic B-spline surfaces This method provides a smooth surface model, yet realises efficient data reduction

Multivariate interpolating (m, l, s)-splines

Abstract: The multivariate interpolating (m, l, s)-splines are a natural generalization of Duchon's thin plate splines (TPS). More precisely, we consider the problem of interpolation with respect to some finite number of linear continuous functionals defined on a semi-Hilbert space and minimizing its semi-norm. The (m, l, s)-splines are explicitly given as a linear combination of translates of radial basis functions. We prove the existence and uniqueness of the interpolating (m, l, s)-splines and investigate some of their properties. Finally, we present some practical examples of (m, l, s)-splines for Lagrange and Hermite interpolation.

Piecewise polynomial kernels for image interpolation: a generalization of cubic convolution

Abstract: A well-known approach to image interpolation is cubic convolution, in which the ideal sine function is modelled by a finite extent kernel, which consists of piecewise third order polynomials In this paper we show that the concept of cubic convolution can be generalized We derive kernels of up to ninth order and compare them both mutually and to cardinal splines of corresponding orders From spectral analyses we conclude that the improvements of the higher order schemes over cubic convolution are only marginal We also conclude that in all cases, cardinal splines are superior

Shape-based grey-level image interpolation.

Abstract: The three-dimensional (3D) object data obtained from a CT scanner usually have unequal sampling frequencies in the x-, y- and z-directions. Generally, the 3D data are first interpolated between slices to obtain isotropic resolution, reconstructed, then operated on using object extraction and display algorithms. The traditional grey-level interpolation introduces a layer of intermediate substance and is not suitable for objects that are very different from the opposite background. The shape-based interpolation method transfers a pixel location to a parameter related to the object shape and the interpolation is performed on that parameter. This process is able to achieve a better interpolation but its application is limited to binary images only. In this paper, we present an improved shape-based interpolation method for grey-level images. The new method uses a polygon to approximate the object shape and performs the interpolation using polygon vertices as references. The binary images representing the shape of the object were first generated via image segmentation on the source images. The target object binary image was then created using regular shape-based interpolation. The polygon enclosing the object for each slice can be generated from the shape of that slice. We determined the relative location in the source slices of each pixel inside the target polygon using the vertices of a polygon as the reference. The target slice grey-level was interpolated from the corresponding source image pixels. The image quality of this interpolation method is better and the mean squared difference is smaller than with traditional grey-level interpolation.

Fast on-line B-spline interpolation

Abstract: A computationally inexpensive algorithm for signal interpolation using B-spline functions is presented. Specifically, the convolution between the B-spline coefficients and the B-spline function itself, widely acknowledged as the most costly aspect of B-spline interpolation, is reformulated such that it is directly amenable to implementation at a much lower computational cost (16.25% of the cost of direct evaluation).

High-precision bilinear interpolation

Abstract: A circuit is provided for performing a high-precision bilinear interpolation operation. The circuit includes a first interpolation operator for interpolating two operands representing a pair of texels using a weight high component of a weighting value. The first interpolation operator outputs a first result. A second interpolation operator interpolates the two operands representing the pair of texels using a weight low component of the weighting value. The second interpolation operator outputs a second result. A combination operator, coupled to the first and second interpolation operators, combines the first and second results to form a value of higher precision than that yielded by typical circuit implementations for bilinear interpolation operation.

Method and apparatus for zooming digital images

Abstract: A method and apparatus for magnifying a portion of a digital image on a display screen in either of two ways. The first method includes a two pass scheme, where each of the passes represents an interpolation in x and y direction respectively, cubic interpolation in each direction is approximated using a one dimensional convolution filter followed by linear interpolation. The second method uses a two dimensional convolution filter first, followed by bilinear interpolation. All of the procedures that are used are accelerated using a hardware package which facilitates exceptionally fast execution.

Sample rate converter using polynomial interpolation

Abstract: A sample rate converter for converting the sampling frequency of an input signal from a first frequency to a second frequency. Such a sample rate converter uses interpolation means and a phase locked loop receiving the first and the second sampling frequency. The invention provides a sample rate converter which uses interpolation means implemented as polynomial interpolation means.

Interpolation processor and storage medium recording interpolation processing program

Abstract: PROBLEM TO BE SOLVED: To execute interpolation processing while suppressing the generation of a false color in a color image having high space frequency or an area having the high space frequency in the color image by providing the interpolation processor with a similarity decision means, an interpolation quantity calculation means for calculating the interpolation quantity of a pixel to be interpolated in accordance with the decision result of the similarity decision means or the like. SOLUTION: An optical image acquired by a photographing optical system 12 is applied to an image pickup part 13. An output from the image pickup part 13 is quantized by an A/D conversion part 14 and supplied to an image processing part 15 as the picture data of a color image. The picture data supplied to the image processing part 15 are interpolated by deciding the intensity of similarity in plural directions by using the similarity in plural directions which is calculated by a similarity calculation means, based on a similarity decision means of an interpolation processing part 17, and calculating the interpolation quantity of the pixel to be interpolated in accordance with the decision result by an interpolation quantity calculation means and recorded through a recording part 16.

Subunity coordinate translation with Fourier transform to achieve efficient and quality three-dimensional medical image interpolation.

Abstract: A new approach to the interpolation of three-dimensional (3D) medical images is presented. Instead of going through the conventional interpolation scheme where the continuous function is first reconstructed from the discrete data set and then resampled, the interpolation is achieved with a subunity coordinate translation technique. The original image is first transformed into the spatial-frequency domain. The phase of the transform is then modified with n-1 linear phase terms in the axial direction to achieve n-1 subunity coordinate translations with a distance 1/n, where n is an interpolation ratio, following the phase shift theorem of Fourier transformation. All the translated images after inverse Fourier transformation are then interspersed in turn into the original image. Since windowing plays an important role in the process, different window functions have been studied and a proper recommendation is provided. The interpolation quality produced with the present method is as good as that with the sampling (sinc) function, while the efficiency, thanks to the fast Fourier transformation, is very much improved. The approach has been validated with both computed tomography (CT) and magnetic resonance (MR) images. The interpolations of 3D CT and MR images are demonstrated.

A novel interpolation scheme for quincunx-subsampled images

Abstract: Image interpolation tries to produce a higher-resolution image from an original image with a lower resolution. In this paper, we introduce a frequency-domain zero-masking technique to set a sufficient number of high-frequency transformed coefficients of an image block to zero, based on which an image interpolation scheme for the quincunx sub-sampling lattice is derived. This interpolation scheme finds solid support from the human visual system that is less sensitive to high frequencies than to low frequencies. Its superiority over other existing schemes has been examined under various circumstances where no coding is applied to the original image or the original image is coded at a (very) low bit-rate.

Efficient image resizing using finite differences

Abstract: We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary scaling factors. This projection-based approach is realizable thanks to a new finite difference method that allows the computation of inner products with analysis functions that are B-splines of any degree n. For a given choice of basis functions, the results of our method are consistently better that those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal-to-noise ratio.

Interpolation by Splines on Triangulations

Abstract: We review recently developed methods of constructing Lagrange and Hermite interpolation sets for bivariate splines on triangulations of general type. Approximation order and numerical performance of our methods are also discussed.

Use of lagrange interpolation in modeling convective kinematics

Abstract: A new procedure for developing higher-order representation of cell interface convective flux based on Lagrange interpolation is presented. The higher-order terms may include any number of nodes across the interface and can be used for uniform and nonuniform grids without loss of generality. The properties of Lagrange interpolation are used to present the higher-order terms as a combination of first-order terms and linearized source terms. This technique satisfies the Scarborough criterion for discretized coefficients automatically. Two popular higher-order schemes, namely, SOU (Second-Order Upwind) and QUICK(Quadratic Upstream Interpolation for Convective Kinematics), are used to illustrate the details of the procedure.

Compensation of unidirectional geometric distortion in EPI using spline warping

Abstract: Due to magnetic field inhomogeneities, EPI images are geometrically distorted, predominantly along the phase-encoding direction. Currently, the distortion is either ignored or compensated manually using a warping function defined through a set of landmarks. We propose an automatic method to unwarp the geometric distortion of EPI images by registering them with corresponding undistorted anatomical MRI images. We show that cubic splines are optimal interpolating functions for both landmark interpolation and approximation. We will consequently use the same warping space in our algorithm which replaces landmarks by an image difference criterion. B-splines are used as generating functions, which leads to a fast and accurate computation. Multiresolution gives robustness and additional speedup. The algorithm performance was evaluated using both real and synthetic data and was found superior to the manual method.

A novel interpolation scheme for rectangularly-subsampled images

Abstract: Image interpolation is perhaps the only way to produce higher-resolution images from an original image with a lower resolution. A frequency-domain zero-masking technique was developed for interpolating hexagonally (or quincunx) subsampled images, with quite promising performances (particularly at low bit rates). In this paper, we focus on an interpolation scheme based on the same technique for another commonly used subsampling lattice-the rectangular grid. To this end, we propose a two-step spatial-domain interpolation in which each step consists of a hexagonal grid. Extensive simulations show that this scheme can provide excellent results in (very) low bit-rate interpolative JPEG coding.