Four commonly used digital halftone algorithms
As we all know, digital halftone technology refers to a technology that realizes the optimal reproduction of images on binary (or multicolor binary) color rendering equipment based on human visual characteristics and image rendering characteristics, using tools such as mathematics and computers. . Digital halftone uses the low-pass characteristics of the human eye. When viewed at a certain distance, the human eye regards the spatially close parts of the image as a whole. With this feature, the local average grayscale of the halftone image observed by the human eye is similar to the local average grayscale value of the original image, thereby forming the effect of continuous tone as a whole.
Halftone technology has been used in the printing field for more than a century, and it has also been used in digital output devices for more than 40 years. As digital output devices such as laser printers, inkjet printers, digital printers, digital cameras, and plasma display screens become more and more popular, digital halftone technology has received widespread attention from manufacturers and research institutions. In addition to the application of digital halftone technology in printing and image output, it is also used in compression storage, textile and medical fields. Therefore, digital halftone technology has important theoretical significance and use value.
According to the application characteristics of digital halftone and different fields, many algorithms have been proposed. When it is classified according to the processing method of the algorithm, it can be divided into point processing algorithm, neighborhood processing algorithm and iterative method. The dot processing algorithm is the simplest method. This type of algorithm uses digital methods to simulate the traditional contact screening process in the printing industry. Each pixel unit in the halftone image produced by it depends only on the pixel tone. The most important methods are the halftone template method and the dithering method; the neighborhood processing algorithm calculates multiple pixels in the neighborhood of the pixels to be processed in the continuous tone image to obtain the pixel values ​​of the halftone image. The most typical of these algorithms is the error diffusion algorithm; the iterative method is an iterative processing algorithm, which requires multiple comparison calculations to obtain the optimal halftone image. Therefore, its calculation is the largest. Here are four representative digital halftone algorithms:
1. Dot Diffusion
The point diffusion halftone algorithm proposed by Knuth is an algorithm that attempts to preserve the advantages of error diffusion while providing parallel processing. The point diffusion algorithm has only one design parameter, the class matrix C, which determines the order in which the pixels are processed by halftone. The position of a continuously adjusted image pixel is divided into the IJ class, and I and J are constant integers.
2. Iterative halftone algorithm
The idea of ​​the iterative halftone algorithm is to use a simple method to obtain the initial halftone image first, and then iteratively process the initial halftone image, so that the halftone image obtained by each processing has a smaller error, and finally the visual most Excellent halftone image. The advantage of the iterative halftone algorithm is that the resulting halftone image has a very good visual effect and basically has no structural texture; it can correctly reproduce rich tones. However, based on the computational complexity of this algorithm, the iterative halftone algorithm is generally difficult to use in real-time processing, and can only be used as a standard test program.
3. Error Diffusion
The error diffusion algorithm is a popular algorithm with better halftone effect. This algorithm was first proposed by Floyed-Steinberg. This algorithm needs to be processed in the neighborhood. It can provide higher halftone quality for the printing machine without causing dot increase. The resulting halftone image has rich tones and the distribution of pixels is anisotropic.
The basic idea is to first quantize the image pixels according to a certain scan path threshold, and then diffuse the quantization error to adjacent unprocessed pixels in a certain way.
DBS uses an iterative exchange procedure to reduce the error E. This algorithm starts from the randomly obtained initial halftone image, scans the entire halftone image in order from left to right, and from top to bottom. For each halftone image For pixels, evaluate the effect of inverting the pixels and swapping their values ​​with the surrounding eight pixels on the quality of the resulting halftone image. If any change reduces the error, the transformation that reduces the error is retained, and the above process is repeatedly performed on the halftone image until there is no conversion operation in the entire process, and the DBS algorithm ends.
4. Ordered dither algorithm (ordered dither)
In this screening algorithm, the input image is compared with a periodic threshold matrix (or called screening matrix). Threshold matrix, where N defines the period of the threshold matrix.
For a particular threshold matrix t (n), the ordered jitter screening algorithm can be described as follows:
The input image should be normalized, ie 0≤x (n) ≤1. When h (n) = 0, the pixels output by halftone are white dots; when h (n) = 1, the pixels output by halftone are black dots. The threshold matrix determines the order in which the dots become black dots when the brightness decreases, and it also determines the quality of the halftone image. The ordered dithering algorithm has different characteristics with different designs of the threshold matrix. The simplest threshold matrix is ​​a matrix in which each pixel is a fixed value: t (n) = 0.5. If an ordered dithering algorithm with such a threshold matrix is ​​implemented on the image, most of the details of the continuous tone image are lost, and the corresponding halftone image obtained has a large distortion compared with the original continuous tone image.
Generally speaking, ordered jitter is divided into point aggregation ordered jitter and point discrete ordered jitter. The screening matrix of dot-gathered ordered dithering is carefully designed to simulate the halftone processing process. When the pixel density of a continuous tone image decreases, dots will be generated around the pixels. The design rule of point discrete ordered dithering is proposed by Bayer. His research pointed out that the visibility of non-ideal artificial textures can be obtained by Fourier analysis of dot patterns at different brightness levels. When a dot pattern of a uniform color block has components at different wavelengths, the component corresponding to the longest wavelength among the limited wavelengths is the component with the highest visibility. Based on this standard, Bayer designed an optimized screening matrix, and the halftone image obtained by applying the point discrete ordered dithering of this matrix contains more visible details.
Although the dot-discrete ordered dithering retains more details, due to the "dot increase", the dot-aggregated ordered dithering is often used in practical applications. The increase in dots is caused by the non-ideal characteristics of the printer. Although it can be assumed that an ideal printer can generate dots with a predefined geometry such as a square, dots will be generated due to the diffusion of ink from the predefined geometry to surrounding pixels Increase the phenomenon. When the pixel density of the continuously-adjusted image decreases, dots will be generated from surrounding pixels, so the orderly dithering of dot aggregation is more likely to prevent the increase of dots, thereby reducing the dot increase effect in the halftone image as a whole.
In general, among these halftone algorithms, the best halftone image quality is the iterative algorithm, but due to the too complicated calculation, it is generally not used in real-time processing algorithms. The error diffusion algorithm is currently the most popular halftone algorithm. The halftone image produced by it has no obvious moire, and the visual effect is better. The dithering algorithm is simple to implement, but it has certain defects in tone reproduction, spatial resolution, and visible texture. The point diffusion algorithm implements parallel processing, but the quality of halftone images needs to be improved.
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