In computer graphics and digital imaging, image scaling is the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement. When scaling a vector graphic image, the graphic primitives that make up the image can be rendered using geometric transformations at any resolution with no loss of image quality. When scaling a raster graphics image, a new image with a higher or lower number of pixels must be generated. In the case of decreasing the pixel number (scaling down), this usually results in a visible quality loss. From the standpoint of digital signal processing, the scaling of raster graphics is a two-dimensional example of sample-rate conversion, the conversion of a discrete signal from a sampling rate (in this case, the local sampling rate) to another.
Mathematical Image scaling can be interpreted as a form of image resampling or image reconstruction from the view of the Nyquist sampling theorem. According to the theorem, downsampling to a smaller image from a higher-resolution original can only be carried out after applying a suitable 2D anti-aliasing filter to prevent aliasing artifacts. The image is reduced to the information that can be carried by the smaller image. In the case of up sampling, a reconstruction filter takes the place of the anti-aliasing filter.
A more sophisticated approach to upscaling treats the problem as an inverse problem, solving the question of generating a plausible image that, when scaled down, would look like the input image. A variety of techniques have been applied for this, including optimization techniques with regularization terms and the use of machine learning from examples.
Algorithms
An image size can be changed in several ways.
Nearest-neighbor interpolation One of the simpler ways of increasing image size is nearest-neighbor interpolation, replacing every pixel with the nearest pixel in the output; for upscaling, this means multiple pixels of the same color will be present. This can preserve sharp details but also introduce jaggedness in previously smooth images. 'Nearest' in nearest-neighbor does not have to be the mathematical nearest. One common implementation is to always round toward zero. Rounding this way produces fewer artifacts and is faster to calculate. This algorithm is often preferred for images which have little to no smooth edges. A common application of this can be found in pixel art.
Bilinear and bicubic interpolation Bilinear interpolation works by interpolating pixel color values, introducing a continuous transition into the output even where the original material has discrete transitions. Although this is desirable for continuous-tone images, this algorithm reduces contrast (sharp edges) in a way that may be undesirable for line art. Bicubic interpolation yields substantially better results, with an increase in computational cost.
Sinc and Lanczos resampling Sinc resampling, in theory, provides the best possible reconstruction for a perfectly bandlimited signal. In practice, the assumptions behind sinc resampling are not completely met by real-world digital images. Lanczos resampling, an approximation to the sinc method, yields better results. Bicubic interpolation can be regarded as a computationally efficient approximation to Lanczos resampling.
Box sampling One weakness of bilinear, bicubic, and related algorithms is that they sample a specific number of pixels. When downscaling below a certain threshold, such as more than twice for all bi-sampling algorithms, the algorithms will sample non-adjacent pixels, which results in both losing data and rough results. The trivial solution to this issue is box sampling, which is to consider the target pixel a box on the original image and sample all pixels inside the box. This ensures that all input pixels contribute to the output. The major weakness of this algorithm is that it is hard to optimize.
Mipmap Another solution to the downscale problem of bi-sampling scaling is mipmaps. A mipmap is a prescaled set of downscaled copies. When downscaling, the nearest larger mipmap is used as the origin to ensure no scaling below the useful threshold of bilinear scaling. This algorithm is fast and easy to optimize. It is standard in many frameworks, such as OpenGL. The cost is using more image memory, exactly one-third more in the standard implementation.
Fourier-transform methods Simple interpolation based on the Fourier transform pads the frequency domain with zero components (a smooth window-based approach would reduce the ringing). Besides the good conservation (or recovery) of details, notable are the ringing and the circular bleeding of content from the left border to the right border (and the other way around).
Edge-directed interpolation Edge-directed interpolation algorithms aim to preserve edges in the image after scaling, unlike other algorithms, which can introduce staircase artifacts. Examples of algorithms for this task include New Edge-Directed Interpolation (NEDI), Edge-Guided Image Interpolation (EGGI), Iterative Curvature-Based Interpolation (ICBI), and Directional Cubic Convolution Interpolation (DCCI). A 2013 analysis found that DCCI had the best scores in peak signal-to-noise ratio and structural similarity on a series of test images.
hqx For magnifying computer graphics with low resolution and/or few colors (usually from 2 to 256 colors), better results can be achieved by hqx or other pixel-art scaling algorithms. These produce sharp edges and maintain a high level of detail.
Vectorization Vector extraction, or vectorization, offers another approach. Vectorization first creates a resolution-independent vector representation of the graphic to be scaled. The resulting SVG vector file can then be exported and rendered at any required resolution without quality loss, serving directly as production-ready artwork for scalable display & printing. This technique is used by Adobe Illustrator, Live Trace, and Inkscape. Scalable Vector Graphics are well suited to simple geometric images, while photographs do not fare well with vectorization due to their complexity.
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