实验要求：

Image Printing Program Based on Halftoning

Objective:

To know in principle what is “halftoning”, the definition of resolution, and how to print an image in a mono-chromosome printer.

Main requirements:

Ability of programming with C, C++, or Matlab.

Instruction manual:

The following figure shows ten shades of gray approximated by dot patterns. Each gray level is represented by a 3 x 3 pattern of black and white dots. A 3 x 3 area full of black dots is the approximation to gray-level black, or 0. Similarly, a 3 x 3 area of white dots represents gray level 9, or white. The other dot patterns are approximations to gray levels in between these two extremes. A gray-level printing scheme based on dots patterns such as these is called “halftoning.” Note that each pixel in an input image will correspond to 3 x 3 pixels on the printed image, so spatial resolution will be reduced to 33% of the original in both the vertical and horizontal direction. Size scaling as required in (a) may further reduce resolution, depending on the size of the input image.

(a) Write a halftoning computer program for printing gray-scale images based on the dot patterns just discussed. Your program must be able to scale the size of an input image so that it does not exceed the area available in a sheet of size 8.5 x 11 inches (21.6 x 27.9 cm). Your program must also scale the gray levels of the input image to span the full halftoning range.

(b) Write a program to generate a test pattern image consisting of a gray scale wedge of size 256 x 256, whose first column is all 0’s, the next column is all 1’s, and so on, with the last column being 255’s. Print this image using your gray-scale printing program.

(c) Print book Figs. 2.22(a) through (c) using your gray-scale printing program. Do your results agree with the conclusions arrived at in the text in pgs. 61-62 and Fig. 2.23? Explain. You will need to download Figs. 2.22(a) through (c).

实验要求是英文的，不懂的词查查字典就行了，这里就不翻译了。

这里简单介绍一下：

Halftoning， 意思是半色调（技术），而在前面的英文实验要求中详细介绍了其原理。

我们主要看下面这幅图：



假设一幅灰度图像，那么我们知道它的每个像素都有一个对应的灰度值，通常这个灰度的取值范围是 0 ~ 255，即 8 bit 灰度级。而半色调技术的意思就是，如图中所示，将灰度级压缩，划分成 10 个灰度级，取值范围是 0 ~ 9。我们想将以前的图像的一个像素，用现在的一个 3 * 3的矩阵表示，它在原图像中的像素值是一个 0 ~ 255 的数， 在 0 ~ 255 内10等分，即像素灰度值除以25.6，则其像素值就会对应图中的某一种情况，那么就用那个矩阵来表示这个像素。比如灰度是 0， 那么那个像素就用图中 0 的情况的矩阵表示。

程序实现不难，不多说直接上代码吧：

%%

    clear all;

    clc;

    close all;

%% 生成一个大小为 256 *256 的简便灰度图像

    s = 256;

    y = zeros(s,s);

    % 每行对应一个灰度级

    for (i=1:s)

        y(i,:)=(255-i-1)*ones(1,s);

    end

    y=uint8(y);

    imwrite(y,'general_img.jpg');

%% 基于半色调计数的图像打印程序

%     x = imread('general_img.jpg');  %读取图片

    x = imread('gray_image.jpg');  %读取图片

    figure(1)

    imshow(x);

    title('original_image');

    [r, c] = size(x);   % 获取图片大小

    % 判断图片大小是否超过 272 * 352， 若超过则进行调整

    r_scale = double(r) / 272;

    c_scale = double(c) / 352;

    scale = max(r_scale, c_scale);  % 找出较大的，后面进行压缩

    % 若图像过大，进行压缩

    if(scale > 1)

       x = imresize(x, 1.0 / scale );

       imwrite(x, 'adjusted_img.jpg');

    end

    figure(2)

    imshow(x);

    title('adjusted_image');

%% 将256灰度级量化成10灰度级别

    [ry, cy] = size(x);     % 获取图片大小

    qim = fix( double(x) / 25.6 );  % 四舍五入。灰度级减小到10灰度级，取整数形式。

    y = zeros(ry*3, cy*3);  % 创建新图片

    % 构造点模式表示10个灰度级

    dot_mat(:,:,1)=zeros(3,3);

    dot_mat(:,:,2)=[0 255 0;0 0 0;0 0 0];

    dot_mat(:,:,3)=[0 255 0;0 0 0;0 0 255];

    dot_mat(:,:,4)=[255 255 0;0 0 0;0 0 255];

    dot_mat(:,:,5)=[255 255 0;0 0 0;255 0 255];

    dot_mat(:,:,6)=[255 255 255;0 0 0,;255 0 255];

    dot_mat(:,:,7)=[255 255 255;0 0 255,;255 0 255];

    dot_mat(:,:,8)=[255 255 255;0 0 255;255 255 255];

    dot_mat(:,:,9)=[255 255 255;255 0 255;255 255 255];

    dot_mat(:,:,10)=[255 255 255;255 255 255;255 255 255];

    % 对每个图像进行点阵映射

    for (i = 1:ry)

        for (j = 1:cy)

            level = qim(i, j);  % 去除灰度级

            y((i-1)*3+1:i*3,(j-1)*3+1:j*3)=dot_mat(:,:,level+1);

        end

    end

    y = uint8(y);

    figure(3)

    imshow(y);

    title('halftoning');

    imwrite(y,'halftoning.jpg');

实验结果：

第一张图片是原图像；

第二张图片是调整大小后的图像，由于使用半色调技术会将原图像放大，所以事先将图片大小缩小一些，避免使用半色调技术后生成的图像过大；

第三张图片就是结果， 也可以在当前文件夹目录下查看程序生成的halftoning.jpg图片。