4. Camera Model & Camera Distortion
15 Jun 2020 | Visual SLAM
Camera and Image
- Visual SLAM(Camera-based)
- Robot uses camera images as a means to observe the outside world(机器人使用相机图像作为观察外界的手段)
- Camera records real-world color and brightness information in pixels(相机以像素为单位记录现实世界的颜色和亮度信息)
- In a three-dimensional world, light is reflected and emitted by objects(在三维世界中，光被物体反射和发射。)
- Light received through the lens is projected onto the camera’s image sensor (e.g., CCD, CMOS)(通过镜头接收的光会投射到相机的图像传感器（例如CCD，CMOS）上)
- Photodiode reacts to convert the detected light intensity and position into digital information(光电二极管起反应，将检测到的光强度和位置转换为数字信息)
- Reconstructed/stored as a digital image through an image processing engine (通过图像处理引擎重建/存储为数字图像)
- For Visual SLAM, a geometric model of the process in which a point in 3D space is projected onto a 2D image plane(对于Visual SLAM，是将3D空间中的点投影到2D图像平面上的过程的几何模型)
- Word Coordinate to image plane
- A process in which a point in 3D space is projected onto a 2D image plane(将3D空间中的点投影到2D图像平面上的过程)
- World coord to a point 상의 in 3D space. Expressed in coordinates 𝑷_w(世界坐标到3D空间中的point点。 以坐标𝑷_w表示)
Pinhole Camera Model
- The mathematical relationship between the coordinates of a point in three-dimensional space and its projection onto the image plane of an ideal pinhole camera, where the camera aperture is described as a point and no lenses are used to focus light.(三维空间中的点的坐标与其在理想针孔相机的图像平面上的投影之间的数学关系，其中相机光圈被描述为一个点，并且没有使用透镜来聚焦光线。)
- Projection of a 3D point onto the image plane(将3D点投影到图像平面上)
- Relationship between the point 𝑷_c and in the three-dimensional space expressed in the camera coordinate system and the image plane(相机坐标系中表示的三维空间中的点𝑷_c与像平面之间的关系)
- Physical image plane to uv image plane(物理图像平面到uv图像平面)
- Sampling and quantization are performed in the process of converting the light detected by the physical imaging sensor into pixels on the digital image plane.(在将由物理成像传感器检测到的光转换为数字图像平面上的像素的过程中执行采样和量化)
Camera Distortion
-
Distortion correction plays a very important role in the field of image processing and image (image) utilization.(失真校正在图像处理和图像（图像）利用领域中起着非常重要的作用。)
-
Image distortion is a serious problem in guessing real-world information from images acquired by a camera(在从相机获取的图像中猜测真实信息时，图像失真是一个严重的问题。)
-
As shown in the figure, the degree of distortion in grasping the shape of the road and building from the image or estimating the location is linked to the error level of the estimated result.(如图所示，从图像中把握道路和建筑物的形状或估计位置时的变形程度与估计结果的误差水平相关。)
Definition of Distortion
-
현실(3차원)세계의 정보를 이미지(2차원)로 투영하는 과정에서 렌즈의 형상(구면)이 Image Plane(평면)에 빛을 올바르게 전달하지 못하여 수차(Aberration) 발생
- 이미지의 왜곡은 크게 두 가지로 구분한다.
- 왜곡(Distortion) : 상(Plane)의 가장자리에 있는 직선을 휘어져 보이게 만드는 렌즈의 수차
- 원근 왜곡(Perspective Distortion) : 렌즈가 피사체에 아주 가깝게 접근했을 때(광각 효과), 또는 아주 멀리 떨어져 있을 때(망원효과) 발생하는 원근감의 변화
- 왜곡은 다시 크게 방사왜곡(Radial Distortion)과 접선왜곡(Tangential Distortion)으로 구분한다
- 방사왜곡 : 카메라에 사용된 볼록렌즈의 굴절률에 의한 왜곡
- 접선왜곡 : 카메라 이미지 센서와 렌즈의 수평이 맞지 않아서 생기는 왜곡
- 이러한 왜곡을 렌즈왜곡(Lens Distortion)이라고도 부른다
- 일반적으로 이미지의 왜곡은 Normalized Image Plane에서 정의됩니다
- 같은 카메라여도 내부 파라미터의 값이 다르기 때문에, 이러한 영향을 제거한 영역에서 정의가 필요
Radial Distortion & Tangential Distortion
- 방사왜곡은 왜곡의 형태에 따라 술통형왜곡(Barrel Distortion)과 바늘꽂이형 왜곡(Pincushion Distortion)으로 부른다.
Radial Distortion
Tangential Distortion
Distortion represented by a mathematical model
- M 은 즉 켈레브레이션을 할떄 필요한 형상 네모나 동그라미 같은 것을 가르킨다.
Reference
SLAM KR
Camera and Image
- Visual SLAM(Camera-based)
- Robot uses camera images as a means to observe the outside world(机器人使用相机图像作为观察外界的手段)
- Camera records real-world color and brightness information in pixels(相机以像素为单位记录现实世界的颜色和亮度信息)
- In a three-dimensional world, light is reflected and emitted by objects(在三维世界中，光被物体反射和发射。)
- Light received through the lens is projected onto the camera’s image sensor (e.g., CCD, CMOS)(通过镜头接收的光会投射到相机的图像传感器（例如CCD，CMOS）上)
- Photodiode reacts to convert the detected light intensity and position into digital information(光电二极管起反应，将检测到的光强度和位置转换为数字信息)
- Reconstructed/stored as a digital image through an image processing engine (通过图像处理引擎重建/存储为数字图像)
- For Visual SLAM, a geometric model of the process in which a point in 3D space is projected onto a 2D image plane(对于Visual SLAM，是将3D空间中的点投影到2D图像平面上的过程的几何模型)
- Word Coordinate to image plane
- A process in which a point in 3D space is projected onto a 2D image plane(将3D空间中的点投影到2D图像平面上的过程)
- World coord to a point 상의 in 3D space. Expressed in coordinates 𝑷_w(世界坐标到3D空间中的point点。 以坐标𝑷_w表示)
- A process in which a point in 3D space is projected onto a 2D image plane(将3D空间中的点投影到2D图像平面上的过程)
Pinhole Camera Model
- The mathematical relationship between the coordinates of a point in three-dimensional space and its projection onto the image plane of an ideal pinhole camera, where the camera aperture is described as a point and no lenses are used to focus light.(三维空间中的点的坐标与其在理想针孔相机的图像平面上的投影之间的数学关系，其中相机光圈被描述为一个点，并且没有使用透镜来聚焦光线。)
- Projection of a 3D point onto the image plane(将3D点投影到图像平面上)
- Relationship between the point 𝑷_c and in the three-dimensional space expressed in the camera coordinate system and the image plane(相机坐标系中表示的三维空间中的点𝑷_c与像平面之间的关系)
- Physical image plane to uv image plane(物理图像平面到uv图像平面)
- Sampling and quantization are performed in the process of converting the light detected by the physical imaging sensor into pixels on the digital image plane.(在将由物理成像传感器检测到的光转换为数字图像平面上的像素的过程中执行采样和量化)
Camera Distortion
-
Distortion correction plays a very important role in the field of image processing and image (image) utilization.(失真校正在图像处理和图像（图像）利用领域中起着非常重要的作用。)
-
Image distortion is a serious problem in guessing real-world information from images acquired by a camera(在从相机获取的图像中猜测真实信息时，图像失真是一个严重的问题。)
-
As shown in the figure, the degree of distortion in grasping the shape of the road and building from the image or estimating the location is linked to the error level of the estimated result.(如图所示，从图像中把握道路和建筑物的形状或估计位置时的变形程度与估计结果的误差水平相关。)
Definition of Distortion
-
현실(3차원)세계의 정보를 이미지(2차원)로 투영하는 과정에서 렌즈의 형상(구면)이 Image Plane(평면)에 빛을 올바르게 전달하지 못하여 수차(Aberration) 발생
- 이미지의 왜곡은 크게 두 가지로 구분한다.
- 왜곡(Distortion) : 상(Plane)의 가장자리에 있는 직선을 휘어져 보이게 만드는 렌즈의 수차
- 원근 왜곡(Perspective Distortion) : 렌즈가 피사체에 아주 가깝게 접근했을 때(광각 효과), 또는 아주 멀리 떨어져 있을 때(망원효과) 발생하는 원근감의 변화
- 왜곡은 다시 크게 방사왜곡(Radial Distortion)과 접선왜곡(Tangential Distortion)으로 구분한다
- 방사왜곡 : 카메라에 사용된 볼록렌즈의 굴절률에 의한 왜곡
- 접선왜곡 : 카메라 이미지 센서와 렌즈의 수평이 맞지 않아서 생기는 왜곡
- 이러한 왜곡을 렌즈왜곡(Lens Distortion)이라고도 부른다
- 일반적으로 이미지의 왜곡은 Normalized Image Plane에서 정의됩니다
- 같은 카메라여도 내부 파라미터의 값이 다르기 때문에, 이러한 영향을 제거한 영역에서 정의가 필요
Radial Distortion & Tangential Distortion
- 방사왜곡은 왜곡의 형태에 따라 술통형왜곡(Barrel Distortion)과 바늘꽂이형 왜곡(Pincushion Distortion)으로 부른다.
Radial Distortion
Tangential Distortion
Distortion represented by a mathematical model
- M 은 즉 켈레브레이션을 할떄 필요한 형상 네모나 동그라미 같은 것을 가르킨다.
Reference
SLAM KR
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