Simple algorithms and architectures for B-spline interpolation

Sankar, P. V.; Ferrari, Leonard A.

doi:10.1109/34.3889

Cited by 30 publications

(7 citation statements)

References 4 publications

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“…Usually, affine transforms such as magnifications [4], [7], [10], [11], [16], [17], [20], [22] or rotations [1], [8], [9], [14] are used to evaluate interpolation methods. High enlargements up to 4; 5.25; and 8 times ( [11], [16], [22]; [5]; and [4], [10], [22], respectively) as well as 10 or 16 repetitions of the transform ( [20] and [14] respectively) are used to enhance the blurring effects incorporated with interpolation. In this paper, simple expansions in one dimension, different rotations, and complex perspective transforms within the range of clinical applications are used to compare the interpolation methods.…”

Section: Interpolation Tasks In Medical Imagingmentioning

confidence: 99%

Survey: interpolation methods in medical image processing

Lehmann

Gonner

Spitzer

1999

IEEE Trans. Med. Imaging

1,113

632

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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 sinc; 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 x 1 up to 8 x 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 x 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 sinc interpolators, all kernels with N = 6 or larger sizes perform significantly better than N = 2 or N = 3 point methods (p << 0.005). However, the differences within the group of large-sized kernels were not significant. Summarizing the results, the cubic 6 x 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 x 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.

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Section: Interpolation Tasks In Medical Imagingmentioning

confidence: 99%

Survey: interpolation methods in medical image processing

Lehmann

Gonner

Spitzer

1999

IEEE Trans. Med. Imaging

1,113

632

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“…In general, they are defined by directly sampling analytic B-splines with Z-transform, bilinear transform, etc. [14], [15], [16], [17], [18]. For this purpose, the first step consists in discretizing the basis functions.…”

Section: Discrete B-splinesmentioning

confidence: 99%

B-spline based filters for multi-point trajectories planning

Biagiotti

Melchiorri

2010

2010 IEEE International Conference on Robotics and Automation

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In this paper, the relation between B-splines and FIR (Finite Impulse Response) filters is demonstrated and exploited to design a digital filter for trajectory planning, combining the very simple structure and computational efficiency of FIR filters with the flexibility of splines. In particular, the trajectory generator consists of two main elements. The former is devoted to the solution of an optimization problem that, given a set of points to be interpolated (or approximated), provides the control points defining the spline. The latter, a cascade of moving average filters, gives the trajectory profile at each sampling time on the basis of such points. The proposed method has been applied to several robotic and industrial applications, and in this paper two case studies are reported as examples: an industrial robot performing a welding operation and a mobile robot moving in an environment with obstacles. With respect to these tasks, the main features of the trajectory generator are shown: the possibility of planning trajectories with high degree of smoothness (continuity of the derivatives), the possibility of easily changing the duration of the trajectory (and therefore the velocity, acceleration, jerk, etc. of the trajectory) maintaining the same geometric path, the possibility of locally modifying the pre-planned path.

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“…To produce a quality print from a video image, the data density of the video signal must be increased to match the resolution of the printing device. Many well-known algorithms such as pixel replication, bilinear interpolation, and various kinds of high-order spline interpolation' 6 152 / Journal of Electronic Imaging / April 1992 / Vol. 1 (2) An imaging source with lower spatial resolution has relatively lower bandwidth in the Fourier domain.…”

Section: Introductionmentioning

confidence: 99%

An edge-restricted spatial interpolation algorithm

Xue

Winans

Walowit³

1992

J. Electron. Imaging

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This study addresses how to generate high spatial resolution image data from a low spatial resolution imaging source. An edge-restricted spatial interpolation algorithm is developed to increase the image resolution and at the same time to enhance the sharp edges and details from the original imaging source. The algorithm is based on a cubic spline-under-tension interpolation kernel. The weights of the interpolation kernel can be adjusted adaptively according to the edge information in the neighborhood of the interpolated pixels. The algorithm can be applied to a relatively low spatial resolution image source, such as video, to generate highresolution image data for high-quality printing devices.

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Simple algorithms and architectures for B-spline interpolation

Cited by 30 publications

References 4 publications

Survey: interpolation methods in medical image processing

Survey: interpolation methods in medical image processing

B-spline based filters for multi-point trajectories planning

An edge-restricted spatial interpolation algorithm

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