●●● ●●●● ●●●●● ●●●● ●●●●● One image 2D-to-3D ●●●● Using prior knowledge(e. g. face Input image (c) +6则 http://www.wisdom.weizmannac.il/-ronen/papers/ Hassner Basr -Example Based 3D Reconstruction from Single 2D Images. pdf 3D computer vsion techniques v 4b2
3D computer vision techniques v.4b2 16 One image 2D-to-3D ⚫ Using prior knowledge (e.g. face) http://www.wisdom.weizmann.ac.il/~ronen/papers/ Hassner Basri - Example Based 3D Reconstruction from Single 2D Images.pdf
TwO-image 2D-to-3D reconstruction ●●●●● 3D computer vsion techniques v 4b2
3D computer vision techniques v.4b2 17 Two-image 2D-to-3D reconstruction
●●● TwO-image 2D-to-3D reconstruction a000. method: stereo vision ●●●●● ●●●● ● Objectives o Basic idea of stereo vision Stereo reconstruction by epipolar geometry Stereo camera pair calibration(find Fundamental matrix F) o Construct the 3D (graphic) model from 2 images Inside a computer Graphic model 3D computer vsion techniques v 4b2
3D computer vision techniques v.4b2 18 Two-image 2D-to-3D reconstruction method: stereo vision ⚫ Objectives: ⚫ Basic idea of stereo vision ⚫ Stereo reconstruction by epipolar geometry ⚫ Stereo camera pair calibration (find Fundamental matrix F) ⚫ Construct the 3D (graphic) model from 2 images Graphic model Inside a computer
if camera motion is pure translation ●●● ●●●● Triangular calculation ●●●●● ●●●● Left Right object ●●●●● Camera Camera Px(x,y, z) ●●●● ●● Principle Principle By similar triangle axIs axIs w.r.t left camera lens center z (x-b Left Right Image X' Image lane plane elimate x→ f·b Focal Leng th b baseline) Left camera center By similar triangle, (reference point) Horizontal w.r.t right camera lens center Disparity=x-冲R D computer vision techniques v 4b2 One major problem is to locate x' and x' r the correspondence problem
3D computer vision techniques v.4b2 19 ⚫ X’l X’r Focal Length f Object Px(x,y,z) z Left camera center (reference point) Horizontal Disparity=xL -xR b (Baseline) Left Camera Principle axis Right Camera Principle axis Left Image plane Right Image plane , ( ) elimate ( ' l ' r ' ' l r x x = z f x - b x = z f f b x z = x - x ) • By similar triangle, w.r.t left camera lens center By similar triangle, w.r.t right camera lens center if camera motion is pure translation : Triangular calculation One major problem is to locate x’l and x’r The correspondence problem
●●● ●●●● ●●●●● If camera motion is Not pure translation ●●●● ●●●●● Use Epipolar Geometry ●●●● X .Right image_ _ pointTEtleft image_point=0 Left side is the reference Pane-3∏3 Perpendicular to T (X2-y2 Right epipolar line X or txx 2 Left epipolar line left right frame Frame Plane-2 I Plane-1∏ O O e R,T Focal Base line= Focal 3D computer vsion techniques length=f, length-f2
3D computer vision techniques v.4b2 20 If camera motion is NOT pure translation : Use Epipolar Geometry ⚫ X O2 O 1 right Frame Plane-2 2 left Frame Plane-1 1 e1 e2 Left epipolar line Right epipolar line R,T (x1 ,y1 ) (x2 ,y2 ) Left side is the reference Focal length=f1 Focal length=f2 Base line=||T|| Plane-3 3 Perpendicular to TX2 or TX1 ⚫Right_image_pointT*E*left_image_point=0