Normalized Weighting Schemes for Image Interpolation Algorithms

This paper presents and evaluates four weighting schemes for image interpolation algorithms. The first scheme is based on the normalized area of the circle, whose diameter is equal to the minimum side of a tetragon. The second scheme is based on the normalized area of the circle, whose radius is equal to the hypotenuse. The third scheme is based on the normalized area of the triangle, whose base and height are equal to the hypotenuse and virtual pixel length, respectively. The fourth weighting scheme is based on the normalized area of the circle, whose radius is equal to the virtual pixel length-based hypotenuse. Experiments demonstrated debatable algorithm performances and the need for further research.Comment: 8 pages, 14 figure

Stochastic Rounding for Image Interpolation and Scan Conversion

The stochastic rounding (SR) function is proposed to evaluate and demonstrate the effects of stochastically rounding row and column subscripts in image interpolation and scan conversion. The proposed SR function is based on a pseudorandom number, enabling the pseudorandom rounding up or down any non-integer row and column subscripts. Also, the SR function exceptionally enables rounding up any possible cases of subscript inputs that are inferior to a pseudorandom number. The algorithm of interest is the nearest-neighbor interpolation (NNI) which is traditionally based on the deterministic rounding (DR) function. Experimental simulation results are provided to demonstrate the performance of NNI-SR and NNI-DR algorithms before and after applying smoothing and sharpening filters of interest. Additional results are also provided to demonstrate the performance of NNI-SR and NNI-DR interpolated scan conversion algorithms in cardiac ultrasound videos.Comment: 10 pages, 17 figures, 3 tables. International Journal of Advanced Computer Science and Applications, 202

Constructing new control points for Bézier interpolating polynomials using new geometrical approach

Interpolation is a mathematical technique employed for estimating the value of missing data between data points. This technique assures that the resulting polynomial passes through all data points. One of the most useful interpolating polynomials is the parametric interpolating polynomial. Bézier interpolating curves and surfaces are parametric interpolating polynomials for two-dimensional (2D) and three-dimensional (3D) datasets, respectively, that produce smooth, flexible, and accurate functions. According to the previous studies, the most crucial component in deriving Bézier interpolating polynomials is the construction of control points. However, most of the existing strategies constructed control points that produce partial smooth functions. As a result, the approximate values of the missing data are not accurate. In this study, nine new strategies of geometrical approach for constructing new 2D and 3D Bézier control points are proposed. The obtained control points from each new strategies are substituted in the relevant Bézier curve and surface equations to derive Bézier piecewise and non-piecewise interpolating polynomials which leads to the development of nine new methods. The proposed methods are proven to preserve the stability and smoothness of the generated Bézier interpolating curves and surfaces. In addition, the numerical results show that most of the resulting polynomials are able to approximate the missing values more accurately compared to those derived by the existing methods. The Bézier interpolating surfaces derived by the proposed method with highest accuracy for 3D datasets are then applied to upscale grey and colour images by the factors of two and three. Not only does the proposed method produces higher quality upscaled images, the numerical results also show that it outperforms the existing methods in terms of accuracy. Therefore, this study has successfully proposed new strategies for constructing new 2D and 3D control points for deriving Bézier interpolating polynomials that are capable of approximating the missing values accurately. In terms of application, the derived Bézier interpolating surfaces have a great potential to be employed in image upscaling

Image Interpolation via Gradient Correlation-Based Edge Direction Estimation

This paper introduces an image interpolation method that provides performance superior to that of the state-of-the-art algorithms. The simple linear method, if used for interpolation, provides interpolation at the cost of blurring, jagging, and other artifacts; however, applying complex methods provides better interpolation results, but sometimes they fail to preserve some specific edge patterns or results in oversmoothing of the edges due to postprocessing of the initial interpolation process. The proposed method uses a new gradient-based approach that makes an intelligent decision based on the edge direction using the edge map and gradient map of an image and interpolates unknown pixels in the predicted direction using known intensity pixels. The input image is subjected to the efficient hysteresis thresholding-based edge map calculation, followed by interpolation of low-resolution edge map to obtain a high-resolution edge map. Edge map interpolation is followed by classification of unknown pixels into obvious edges, uniform regions, and transitional edges using the decision support system. Coefficient-based interpolation that involves gradient coefficient and distance coefficient is applied to obvious edge pixels in the high-resolution image, whereas transitional edges in the neighborhood of an obvious edge are interpolated in the same direction to provide uniform interpolation. Simple line averaging is applied to pixels that are not detected as an edge to decrease the complexity of the proposed method. Applying line averaging to smooth pixels helps to control the complexity of the algorithm, whereas applying gradient-based interpolation preserves edges and hence results in better performance at reasonable complexity