Streo Vision

Characteristics of Stereo Vision

• 3D reconstruction
  • Shading, focus/defocus, texture, perspective effects, motion, occlusion, stereo
• Human stereopsis
  • fixation, disparity
• Multiple views
  • epipolar geometry
• Stereo Vision
  • geometry of a parallel stereo system
  • correspondence

Methods of 3D reconstruction

• Dimensionality Reduction

  The spatial information is lost while 3D object is projected to 2D. In that case, lengths are lost and angle preservation is lost. Hence, Parallel line are lost but there is a vanishing point where two lines, which was once parallel line, meet together.

  From this vanishing point, we can find out and track the spatial information lost.

Figure1. Dimensinality reduction

• Structure from Shadow

Figure2. Structure from Shadow

• Lmertian Reflectance Model for approximating the reflectance property of the diffuse surface

\[Diffuse\; Surface\; Color = \frac{\rho_d}{\pi} *L_i * cos{\theta}\]

Light from all points on the surface reaches the viewer (camera). It means we can deduce the 3D surface from intensity and angles.

• Structure from focus

Figure3. Structure from focus

Despite the same images, we can deduce 3D information while using low-pass filter with different sigma to make images blur or not.

• Texture

Figure4. Structure form Texture

We can infer the 3D data while measuring images pattern. e.g. If the white seeds of strawberry is close, it means the distance is close. If the white seeds of strawberry is far, it means the distance is far.

• Perspective effects

Figure5. Vanishing point

Perspective effect means even paraller line converge on one point while 3D image is prjected to 2D image. We can infer spatial information from vanishing point. the side effect of this method,However, is there is foriegn objects of air and the signal is hard to reach on camera. e.g.) when we take a mountain photo, the more the object is far from the camera, the more ambiguous the object is.

• Stereo

Figure6. Stereo Vision

It is important to note that the camera centor should be moved not fixed with rotation in Stereo Vision for obtaining exact 3D information.

Disparity

Figure7. Human steropsis: disparity

disparity occurs when eyes fixate on one object; others appear at different visual angles. Disparity is distance from b1 to b2 along retina.

Multiple views

Why we have multiple views? Because there is distortion when projection occurs. e.g. the line which is connected the optical center of camera is projected to one point, not line.

Figure8. Multiple views

In multiple views, we shift the projection image to infront of the optical center than using pin hole model which change the locations for 2D coordinate,as an ideal mathematic method.

Stereo Vision

Figure9. Epipolar Geometry

epipole - when the line which connects optical centers of two cameras, e and e’ are called to epipoles. epipolar line - the line which connects epipole and point projected. epipolar constraint - Depending on DOF(Degree of Freedom), there are the 8,7,5,3 and 1 pair of matching points to obtain fundamental and essential matrix. Triangulation - If we know E, F matrix and p,p’, we can obtain 3D point.

Reference

• https://www.youtube.com/watch?v=3QjEOlfvg9M&t=2326
• https://math.hws.edu/graphicsbook/c4/s1.html