Bicubic interpolation

About: Bicubic interpolation is a research topic. Over the lifetime, 3348 publications have been published within this topic receiving 73126 citations.

General Properties of Interpolation Spaces

Abstract: In this chapter we introduce some basic notation and definitions. We discuss a few general results on interpolation spaces. The most important one is the Aronszajn-Gagliardo theorem.

Fast and Accurate Image Super-Resolution with Deep Laplacian Pyramid Networks

Abstract: Convolutional neural networks have recently demonstrated high-quality reconstruction for single image super-resolution. However, existing methods often require a large number of network parameters and entail heavy computational loads at runtime for generating high-accuracy super-resolution results. In this paper, we propose the deep Laplacian Pyramid Super-Resolution Network for fast and accurate image super-resolution. The proposed network progressively reconstructs the sub-band residuals of high-resolution images at multiple pyramid levels. In contrast to existing methods that involve the bicubic interpolation for pre-processing (which results in large feature maps), the proposed method directly extracts features from the low-resolution input space and thereby entails low computational loads. We train the proposed network with deep supervision using the robust Charbonnier loss functions and achieve high-quality image reconstruction. Furthermore, we utilize the recursive layers to share parameters across as well as within pyramid levels, and thus drastically reduce the number of parameters. Extensive quantitative and qualitative evaluations on benchmark datasets show that the proposed algorithm performs favorably against the state-of-the-art methods in terms of run-time and image quality.

Mesh-Independent Surface Interpolation

Abstract: Smooth interpolation of unstructured surface data is usually achieved by joining local patches, where each patch is an approximation (usually parametric) defined on a local reference domain. A basic mesh-independent projection strategy for general surface interpolation is proposed here. The projection is based upon the ’Moving-Least-Squares’ (MLS) approach, and the resulting surface is C ∞ smooth. The projection involves a first stage of defining a local reference domain and a second stage of constructing an MLS approximation with respect to the reference domain. The approach is presented for the general problem of approximating a (d − 1)-dimensional manifold in ℝ d , d ≥ 2. The approach is applicable for interpolating or smoothing curve and surface data, as demonstrated here by some graphical examples.

Edge-directed interpolation

Abstract: We present a new method for digitally interpolating images to higher resolution. It consists of two phases: rendering and correction. The rendering phase is edge-directed. From the low resolution image data, we generate a high resolution edge map by first filtering with a rectangular center-on-surround-off filter and then performing piecewise linear interpolation between the zero crossings in the filter output. The rendering phase is based on bilinear interpolation modified to prevent interpolation across edges, as determined from the estimated high resolution edge map. During the correction phase, we modify the mesh values on which the rendering is based to account for the disparity between the true low resolution data, and that predicted by a sensor model operating on the high resolution output of the rendering phase. The overall process is repeated iteratively. We show experimental results which demonstrate the efficacy of our interpolation method.

Algorithms for subpixel registration

Abstract: This paper presents an analysis of four algorithms which are able to register images with subpixel accuracy; these are correlation interpolation, intensity interpolation, differential method, and phase correlation. The subpixel registration problem is described in detail and the resampling process for subpixel registration is analyzed theoretically. It is shown that the main factors affecting registration accuracy are the interpolation function, sampling frequency, number of bits per pixel, and frequency content of the image. An iterative version of the intensity interpolation algorithm, which achieves maximum computational efficiency, is also presented. Analyses, computer simulations, and experiments for measuring displacements of objects using their speckle images have shown that this algorithm is faster than a direct intensity interpolation algorithm by a factor of more than ten thousand. Using bilinear interpolation and representing pixels by 8-bit samples, a 0.01 to 0.05 pixel registration accuracy can be achieved.