图形学笔记《Fundamentals of Computer Graphics 4th Edition》——【3】Raster Images 光栅图像

raster display: show images as rectangular arrays of pixels
pixel: a short for “picture element”
raster image: a 2D array that stores the pixel value for each pixel——R G B
因为显示设备与图片大小不能保证一致，可能会有拉伸、变形、变色等变换发生，因此it’s best to think of a raster image as a device-independent description of the image to be displayed
vector image: 另一种显示方式，storing descriptions of shapes——areas of color bounded by lines or curves——with no reference to any particular pixel grid
- advantage: resolution independent, can be displayed well on very high resolution devices
- disadvantage: must be rasterized（光栅化） before displayed
- often used for: text, diagrams, mechanical drawings——crispness and precision are important, photographic images and complex shading aren’t needed

一般说来，显示设备有两种：

emissive displays: 发射型显示器，use pixels that directly emit controllable amounts of light
- 如，light-emitting diode (LED), 每个像素上都有半导体设备（可能多个颜色如R G B，在远方看起来就会形成一种颜色），根据当前电流决定其光强
transmissive displays: 透射式显示器，the pixels themselves don’t emit light but instead vary the amount of the light that they allow to pass through them, require a light source to illuminate them
- 如，liquid crystal displays (LCDs)，如图所示，偏振光会根据电压大小偏转不同的角度，偏转度为0时没有光线通过filter，当电压使其偏转90度时，所有光线都会通过filter，此时光强最大

int-jet printer: 喷墨式打印机，一般只能打印binary images，可使用多颜色喷头打印彩色图片
thermal dye transfer: 热敏式，在print head和dye receiver中间加入一层donor ribbon，可以根据热度产生不同强度的颜色

分辨率的含义——pixel desity
- ppi: 如热敏式的300 pixels per inch——has elements spaced 300 per inch across its head
- dpi: 如喷墨式的1200 dots per inch——places dots on a grid with 1200 grid points per inch
- 同等质量的图片，喷墨式通常需要比热敏式更高的分辨率（吧？）

相机中也有像素级别的感光元件，去获取该像素的颜色和光强
多数相机中会使用像上图一样的color-filter array or mosaic to allow each pixel to see only red, green or blue light, leaving the image processing software to fill in the missing values in a process known as demosaicking（去马赛克）
还有一些相机使用多层感光元件，每一层去感不同颜色的光（R G B），不需要多余的处理了

分辨率的含义：
- the fixed number of pixels in the array
- is usually quoted using the total count of pixels：如3000×2000 = 6 million pixels——6 megapixel (MP) camera

首先，我们将图片的表示抽象为 $I (x, y) : R \to V$ ，其中 $R \subset R^{2}$ is a rectangular area, V is the set of possible pixel values
像素点的值含义：the value of the image in the vicinity（邻近） of this grid point
下图是本书中像素含义约定：

HDR: high dynamic range, images stored with floating-point numbers
LDR: low dynamic range, images that are stored with integers
常见格式：每像素RGB（3个）/灰度（1个）32位浮点数——占内存太大，所以要优化
但优化后，每像素所用位数变少，可能会造成两种后果：
- clipping: 如，阳光下，过亮的地方无法显示
- quantization, or banding: 尤其在动态图像中，会产生突变

显示值和输入值不是一一对称的，也不是线性关系（显示器关掉的时候可能也会有一点光强）
通常可用公式表示： $d i s p l a y e d i n t e n s i t y = (m a x i m u m i n t e n s i t y) a^{λ}$ , where $a$ is the input pixel value between zero and one, $λ$ is the degree of freedom
$λ$ 的求法：找到灰度=0.5时的a值， $λ = \frac{\ln 0.5}{\ln a}$
这个图还蛮好玩的就放上来啦！离远了看或者摘掉近视眼镜看，觉得左右颜色一样，就找到灰度=0.5的颜色了~
gamma correct原理看懂了，那个公式看不明白。。总觉得不对
原理是，令 $a^{^{'}} = a^{\frac{1}{λ}}$ ，可以使输入输出变成线性~

为什么要有个 $λ$ 值？

图形学笔记《Fundamentals of Computer Graphics 4th Edition》——【3】Raster Images 光栅图像

混合结果可以用公式表示： $c = α c_{f} + (1 - α) c_{b}$ , where $α$ is the pixel coverage, which tells the fraction of the pixel covered by the foreground layer, $c_{f}$ is the foreground color, $c_{b}$ is the background color
$α$ 值可以存储在一个单独的灰度图像中，又可称为alpha mask或transparency mask；或存储在RGB图像的第四个通道中，即alpha channel

jpeg: lossy formant, compresses image blocks based on thresholds in the human visual system, works well for natural images
tiff: is most commonly used to hold binary images or losslessly compressed 8- or 16-bit RGB
ppm: loseless, uncompressed format, most often used for 8-bit RGB images
png: lossless, with a good set of open source management tools