计算机图形学Lec2：图像
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计算机图形学

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颜色模型 Color Model

定义

颜色模型表示一种通过原色集合产生所有颜色范围的系统。
A Color model represents a system to produce all ranges of color through the primary color set.

我们可用 RGB 和 CMYK 模型创建每种颜色。
A Color model is a hierarchical system in which we can create every color by using RGB (Red, Green, Blue) and CMYK (Cyan, Magenta, Yellow, Black) models.


加色模型 Additive Color Model

加色模型也称 RGB 模型，RGB 代表红、绿、蓝。
It is also named as RGB model. RGB stands for Red, Green and Blue.

加色颜色模型用于数字屏幕显示，如计算机屏幕或手机显示。
Additive color model is used for digital screen-based display, like display of an object or a picture in computer screen or in like phone display.

每个原色被赋予 0 到 255 之间的值。
A value between 0 to 255 is assigned to each of the primary color.


减色模型 Subtractive Color Model

减色颜色模型也称 CMYK 模型，CMYK 代表青、品红、黄、黑。
Subtractive Color Model: It is also named as CMYK Model. CMYK stands for Cyan, Magenta, Yellow, and Black.

主要用于打印用途，如打印杂志。
Mainly used for printing purposes like printing a magazine.

图像表示 Image Representation

定义

数字图像被定义为一个二维数组，由像素组成。
A digital image is defined as a 2D array, which is consisting of pixels


图像处理 Image Processing

图像处理是对图像执行某些操作的方法，也用于获得增强图像或从图像中获取一些有用信息。
Image processing is a method to implement some operations (like: binarization, filtering techniques) on an image. It is also used to get an enhanced image or to access some useful information from an image.

示例：照片和视频帧。
For example- photographs, frames of video.


像素 Pixel

像素是计算机屏幕上显示图片的最小单位，也是图像的基本组件或基本构建块。
Pixel is the smallest unit of a picture displayed on the computer screen and basic component or basic building block of an image

图像大小定义为水平方向像素总数乘以垂直方向像素总数，例如 1024 × 768。
The size of the image is defined as the total number of pixels in the horizontal direction times the total number of pixels in the vertical direction, Such as (1024 x 768).

图像宽度与高度之比称为图像宽高比。
The ratio of an image’s width to its height is known as the aspect ratio of the image.

单位面积像素数称为图像分辨率。
The number of pixels per unit is called the resolution of the image.


图像处理应用 Applications of Image Processing

有以下几种应用范围：

  • 计算机化摄影：使用数字计算进行数字图像捕获和处理的技术。
    Computerized Photography- It refers to digital image capture and processing techniques that use digital computation
  • 医学/生物图像处理：分割和疾病检测分析。
    Medical/ Biological Image Processing- segmentation, analysis for decease detection
  • 自动字符识别：数字和字母识别。
    Automatic Character Recognition- recognition of digits and letters
  • 指纹/人脸/虹膜识别：认证和访问控制。
    Fingerprint/ Face/ Iris Recognition- for authentication, access control
  • 遥感：从远距离捕获对象。
    Remote sensing- Capture of objects from distances
  • 工业应用：质量控制和缺陷检测。
    Industrial application- Quality control, defect detection


图像文件格式 Format of Image Files

有以下几种图像文件格式：

  • JPEG 联合图像专家组格式：用于数字图像，尤其是数字摄影组成的图像。
    JPEG (Joint Photographic Experts Group): It is used for digital images, especially for those images which are composed of digital photography.
  • PNG 可移植网络图形格式：常用于存储网页图像图形。
    PNG (Portable Network Graphics): These files are commonly used to store graphics for web images.
  • GIF（图形交换格式）：这是一种用于存储最多256种颜色的图形图像的文件格式。
    GIF (Graphics Interchange Format): It is a file format for storing graphical images up to 256 colors.
  • TIFF/TIF（标签图像文件格式）：用于保障图像的完整性与清晰度，常用于专业摄影领域。
    TIFF/ TIF (Tagged Image File): TIFF file is used to maintain image integrity and clarity.It is often used for professional photography.

图像表示 Image Representation

二维 2D (2-Dimension)

定义

二维图像由具有长度和宽度两个维度的平面表示。
2-dimensional image is represented by a flat plane that has two dimensions length and width.

例如圆、三角形、正方形、矩形和五边形，因为它们有长度和宽度。
Some examples of 2-dimensional are as follows circle, triangle, square, rectangle and pentagon as they have length and width.


二维变换 Transformation for 2D

主要包含以下操作：

  • 平移 Translation
  • 缩放 Scaling
  • 旋转 Rotation
  • 反射 Reflection

二维平移 2D Translation

二维平移是任何对象从一个位置移动到另一个位置而不改变对象形状。
Movement of any object from one to another place without changing the shape of the object.

假如原始点P的坐标为(x0,y0)(x_0,y_0)，新点Q的坐标为(x1,y1)(x_1,y_1)，位移向量 translation vector (or shift vector) 为(Tx,Ty)(T_x,T_y)，那么他们满足

{x0+Tx=x1y0+Ty=y1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0+T_x&=& x_1 \\ y_0+T_y&=& y_1 \end{array}\right. \end{array}

二维缩放 2D Scaling

缩放中任何对象的大小可以扩展或压缩。
In scaling, the size of any object can be expended or compressed.

假如原始点P的坐标为(x0,y0)(x_0,y_0)，新点Q的坐标为(x1,y1)(x_1,y_1)，缩放因子 caling factor 为(Sx,Sy)(S_x,S_y)，那么他们满足

{x0⋅Sx=x1y0⋅Sy=y1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0\cdot S_x&=& x_1 \\ y_0\cdot S_y&=& y_1 \end{array}\right. \end{array}

二维旋转 2D Rotation

二维旋转是改变对象角度的过程。
It is a process of changing the angle of the object.

假如原始点P的坐标为(x0,y0)(x_0,y_0)，新点Q的坐标为(x1,y1)(x_1,y_1)，旋转角度 Rotation angle为θ\theta，那么他们满足

{x0cos⁡θ−y0sin⁡θ=x1x0sin⁡θ+y0cos⁡θ=y1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0\cos\theta -y_0\sin\theta&=& x_1\\x_0\sin\theta +y_0\cos\theta&=& y_1 \end{array}\right. \end{array}

二维反射 2D Reflection

产生对象镜像的变换称为反射。
A transformation that produces a mirror image of an object is called a reflection.

假如原始点P的坐标为(x0,y0)(x_0,y_0)，新点Q的坐标为(x1,y1)(x_1,y_1)，那么对于四种反射，他们分别满足

  • 沿 X 轴反射 Reflection along X-axis {x0=x1y0=−y1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0&=& x_1\\y_0&=& -y_1 \end{array}\right. \end{array}
  • 沿 Y 轴反射 Reflection along Y-axis {x0=−x1y0=y1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0&=& -x_1\\y_0&=& y_1 \end{array}\right. \end{array}
  • 垂直于 XY 平面反射（原点中心对称） Reflection perpendicular to XY plane {x0=−x1y0=−y1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0&=& -x_1\\y_0&=& -y_1 \end{array}\right. \end{array}
  • 关于直线 X=Y 反射 Reflection with respect to a line X=Y {x0=y1y0=x1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0&=& y_1\\y_0&=& x_1 \end{array}\right. \end{array}


三维 3D (3-Dimension)

定义

三维图像或对象由长度、宽度和高度三个维度表示。
3-Dimension image or object is represented by the three dimensions – length, width and height.

三维示例包括立方体、圆锥和圆柱，因为它们有长度、宽度和长度。
Some example of 3 D are as follows cube, cone and cylinder as it has length, width and length.


三维变换 Transformation for 3D

主要包含以下操作：

  • 平移 Translation
  • 缩放 Scaling
  • 旋转 Rotation
  • 反射 Reflection

三维平移 3D Translation

三维平移是任何对象从一个位置移动到另一个位置而不改变对象形状。（PS：我刚刚是不是说过这句话了🤔）
Movement of any object from one to another place without changing the shape of the object.

假如原始点P的坐标为(x0,y0,z0)(x_0,y_0,z_0)，新点Q的坐标为(x1,y1,z1)(x_1,y_1,z_1)，位移向量 translation vector (or shift vector) 为(Tx,Ty,Tz)(T_x,T_y,T_z)，那么他们满足

{x0+Tx=x1y0+Ty=y1z0+Tz=z1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0+T_x&=& x_1 \\ y_0+T_y&=& y_1\\z_0+T_z&=&z_1 \end{array}\right. \end{array}

三维缩放 3D Scaling

缩放中任何对象的大小可以扩展或压缩。
In scaling, the size of any object can be expended or compressed.

假如原始点P的坐标为(x0,y0,z0)(x_0,y_0,z_0)，新点Q的坐标为(x1,y1,z1)(x_1,y_1,z_1)，缩放因子 caling factor 为(Sx,Sy,Sz)(S_x,S_y,S_z)，那么他们满足

{x0⋅Sx=x1y0⋅Sy=y1z0⋅Sz=z1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0\cdot S_x&=& x_1 \\ y_0\cdot S_y&=& y_1 \\z_0\cdot S_z&=&z_1\end{array}\right. \end{array}

三维旋转 3D Rotation

三维旋转是改变对象角度的过程。
It is a process of changing the angle of the object.

假如原始点P的坐标为(x0,y0,z0)(x_0,y_0,z_0)，新点Q的坐标为(x1,y1,z1)(x_1,y_1,z_1)，旋转角度 Rotation angle为θ\theta，那么对于三种旋转，他们分别满足

  • x 轴旋转 x-axis Rotation {x0=x1y0cos⁡θ−z0sin⁡θ=y1y0sin⁡θ+z0cos⁡θ=z1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0&=& x_1\\y_0\cos\theta -z_0\sin\theta&=& y_1 \\y_0\sin\theta +z_0\cos\theta&=& z_1\end{array}\right. \end{array}
  • y 轴旋转 y-axis Rotation {y0=y1z0cos⁡θ−x0sin⁡θ=z1z0sin⁡θ+x0sin⁡θ=x1\begin{array}{rcl} \left\{\begin{array}{rcr} y_0 &=& y_1 \\z_0\cos\theta -x_0\sin\theta&=& z_1\\z_0\sin\theta+x_0\sin\theta&=&x_1\end{array}\right. \end{array}
  • z 轴旋转 z-axis Rotation {z0=z1x0cos⁡θ−y0sin⁡θ=x1x0sin⁡θ+y0sin⁡θ=y1\begin{array}{rcl} \left\{\begin{array}{rcr} z_0 &=& z_1 \\x_0\cos\theta -y_0\sin\theta&=& x_1\\x_0\sin\theta+y_0\sin\theta&=&y_1\end{array}\right. \end{array}

好记的办法：xyz循环


三维反射 2D Reflection

产生对象镜像的变换称为反射。
A transformation that produces a mirror image of an object is called a reflection.

假如原始点P的坐标为(x0,y0,z0)(x_0,y_0,z_0)，新点Q的坐标为(x1,y1,z1)(x_1,y_1,z_1)，那么对于三种反射，他们分别满足

  • 沿 xy 平面反射 Reflection along with xy Plane {x0=x1y0=y1z0=−z1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0&=& x_1\\y_0&=& y_1 \\z_0&=&-z_1 \end{array}\right. \end{array}
  • 沿 xz 平面反射 Reflection along with xz Plane {x0=x1y0=−y1z0=z1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0&=& x_1\\y_0&=& -y_1 \\z_0&=&z_1 \end{array}\right. \end{array}
  • 沿 yz 平面反射 Reflection along with yz Plane {x0=−x1y0=y1z0=z1\begin{array}{rcl} \left\{\begin{array}{rcr} x_0&=& -x_1\\y_0&=& y_1 \\z_0&=&z_1 \end{array}\right. \end{array}

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