What Is Image Scaling?

In computer image processing and computer graphics, image scaling refers to the process of adjusting the size of digital images. Image scaling is a non-trivial process that requires a trade-off between processing efficiency and the resulting smoothness and sharpness. As the size of an image increases, the visibility of the pixels that make up the image becomes higher, making the image appear "soft". Conversely, reducing an image will enhance its smoothness and sharpness.

The main purpose of reducing an image (also called subsampling or downsampling) is twofold: 1. Make the image fit the size of the display area; 2. Generate the corresponding image

Assume the source image looks like this:

To double the image, there are many algorithms. The easiest method is to perform neighborhood interpolation.

Almost all images are enlarged by interpolation, that is, based on the original image pixels, a new element is inserted between pixels using a suitable interpolation algorithm.

Image scaling interpolation algorithm classification

The classification of the interpolation algorithm is confusing, and each person has his own classification algorithm. The document "Overview of Image Interpolation Techniques" briefly classifies interpolation algorithms into three categories: traditional interpolation, edge-based interpolation, and area-based interpolation. As a beginner, clear interpolation algorithms are still helpful.

1. Traditional difference principle and evaluation

In the traditional image interpolation algorithm, neighbor interpolation is simple and easy to implement, and it is more common in the early days. However, this method produces noticeable jagged edges and mosaics in new images. The bilinear interpolation method has a smoothing function, which can effectively overcome the shortcomings of the neighboring method, but it will degrade the high-frequency part of the image and make the details of the image blurred. When the magnification is high, higher-order interpolation, such as bicubic and cubic spline interpolation, is better than low-order interpolation. These interpolation algorithms can make the gray value of the pixels generated by interpolation continue the continuity of the gray change of the original image, so that the change in the density of the enlarged image is naturally smooth. However, in the image, there are abrupt changes in gray values between some pixels and neighboring pixels, that is, there are gray discontinuities. These pixels with abrupt changes in gray value are the edge pixels in the image that describe the outline of the object or the texture image. In image magnification, if these pixels with discontinuous grayscale characteristics are used to generate newly added pixels using conventional interpolation algorithms, the outline and texture of the enlarged image will inevitably be blurred, and the image quality will be reduced.

2.Edge-based image interpolation algorithm

In order to overcome the shortcomings of traditional methods, many edge protection interpolation methods have been proposed, which have some enhancements to the edges of the interpolated image, which makes the image visual effect better. Edge method and method based on interpolation of high-resolution image edges. The method based on the edges of the original low-resolution image : (1) First detect the edges of the low-resolution image, and then classify the pixels based on the detected edges. For pixels in flat areas, use traditional methods to interpolate; for pixels in edge areas, design Special interpolation method to achieve the purpose of maintaining edge details. (2) Interpolation methods based on high-resolution image edges after interpolation : This method uses the traditional method to interpolate low-resolution images, then detects the edges of high-resolution images, and finally performs special processing on edges and nearby pixels to remove blur , Enhance the edges of the image.

3. Region-based image interpolation algorithm

First, the original low-resolution image is divided into different regions, then the interpolation points are mapped to the low-resolution image, and the region to which they belong is determined. Finally, different interpolation formulas are designed according to the neighborhood pixels of the interpolation points to calculate the values of the interpolation points.

Image scaling mainstream interpolation algorithm

The classification methods described in the above literature can be referred to, but the methods described in the literature are too narrow and are based on the improvement of the linear method. Partial differential equation interpolation (PDE), fractal, and wavelet inverse interpolation are also one of the mainstream of interpolation algorithms. Wavelet and fractal algorithms have high computational complexity and good results. Wavelet edge processing is the best, followed by fractal. ^[1]

Wavelet interpolation makes full use of the singularity of image propagation along the wavelet decomposition scale, and can more accurately reconstruct high-resolution image details. However, the singular value localization of wavelet coefficients involves precise and complicated edge detection and the wavelet coefficients are difficult to align across scales, which makes the algorithm implementation very complicated. There are two main algorithms based on wavelet interpolation, which are subband interpolation and extreme value extrapolation. The wavelet transform essentially uses the wavelet function as

The band-pass filter performs filtering, and decomposes the original signal into a series of frequency bands. The wavelet transform is defined by the wavelet function cluster as: Wavelet interpolation formula 1.

Wavelet interpolation formula 1

The inverse wavelet transform is used to transform the signals decomposed into various frequency bands.

Reconstruction of starting signal: wavelet interpolation formula 2

Wavelet interpolation formula 2

Wavelet interpolation formula 3:

Wavelet interpolation formula 3

The two-dimensional discrete wavelet transform is extended to reconstruct and interpolate digital images. If the image is a two-dimensional signal with limited spatial frequency, the image obtained by wavelet inverse transform of the corresponding frequency window on the image can be considered as an interpolation of the image.

A fractal image is an image with complex geometric shapes and irregularities, but its internal basic feature is self-similarity, which reflects the similarity of statistical significance in terms of morphology, function, time and space, etc. between local and local, local and overall. The simple and effective method to improve the image resolution is interpolation, but after normal interpolation, the texture features of the image will be lost.Fractal interpolation methods can be used to generate high-resolution images, while maintaining the texture features of the original image . ^[1]