Efficient cubic spline interpolation implemented with FIR filters
نویسندگان
چکیده
Classical Cubic spline interpolation needs to solve a set of equations of high dimension. In this work we show how to compute the interpolant using a FIR digital filter, with a reduced number of operations per interpolated point and high accuracy. Additionally, the computation can be made on real time as the signal samples are acquired. Following this approach, we show how to obtain easily the derivatives of the interpolant in a similar way, and also signal approximations to reduce the oscillations that appear when using high order splines. These techniques are very well suited to compute continuous representations of image contours on closed shapes and to find its curvature and singularities.
منابع مشابه
FIR approximations of inverse filters and perfect reconstruction filter banks
This paper first describes an algorithm that finds the approximate finite impulse response (FIR) inverse of an FIR filter by minimizing the inversion (or reconstruction) error constrained to zero-bias. The generalization of the inverse filtering problem in the two channel case is the design of perfect reconstruction filter banks that use critical sampling. These considerations lead to the deriv...
متن کاملFast digital zooming system using directionally adaptive image interpolation and restoration
This paper presents a fast digital zooming system for mobile consumer cameras using directionally adaptive image interpolation and restoration methods. The proposed interpolation algorithm performs edge refinement along the initially estimated edge orientation using directionally steerable filters. Either the directionally weighted linear or adaptive cubic-spline interpolation filter is then se...
متن کاملCascade Adaptive Filters and Applications to Acoustic Echo Cancellation
Typical approaches to acoustic echo cancellation (AEC) in mobile telephones employ adaptive linear algorithms, such as the normalized least mean squares (NLMS) algorithm. Smaller, cheaper components on these devices introduce nonlinearities into the echo path, which adversely affect performance of linear AEC systems and necessitate means of nonlinear compensation. Memoryless nonlinear blocks th...
متن کاملEfficient Cubic B-spline Image Interpolation on a GPU
Application of geometric transformation to images requires an interpolation step. When applied to image rotation, the presently most e cient GPU implementation for the cubic spline image interpolation still cost about 10 times as much as linear interpolation. This implementation involves two steps: a pre lter step performs a two-pass forward-backward recursive lter, then a cubic polynomial inte...
متن کاملEvaluation and Design of Filters Using a Taylor Series Expansion
We describe a new method for analyzing, classifying, and evaluating filters that can be applied to interpolation filters as well as to arbitrary derivative filters of any order. Our analysis is based on the Taylor series expansion of the convolution sum. Our analysis shows the need and derives the method for the normalization of derivative filter weights. Under certain minimal restrictions of t...
متن کامل