mage Processing and Computer Vision Chapter 10: Pose estimation by the iterative method Pose estimation vo.a
Image Processing and Computer Vision Chapter 10: Pose estimation by the iterative method Pose estimation V0.a 1
Overview Define the terms Define structure from motion sem Methods for sem Define pose estimation and why we need to study it Newton 's method Iterative algorithm for pose estimation Pose estimation vo.a
Overview • Define the terms • Define Structure From Motion SFM • Methods for SFM • Define pose estimation, and why we need to study it • Newton's method • Iterative algorithm for pose estimation Pose estimation V0.a 2
Intro) I Motivation I Pose est. I Newton's method I Iterative method Define the terms 3 D Model=X1=ⅨXyZ7 where i=feature index X=2=[92,126209] 1 2.N features X can be found by manual Xi=1=[102, 18,23 measurement Pose 6t is the Rotation(R) and Translation(t)of the object at a time t, where u= horizontal image position 3x3/3x1t v=vertical image position gti= lu,v] is the image point of the ith 3D feature at time t Pose estimation vo.a
Intro. | Motivation | Pose est.| Newton’s method | Iterative method Define the terms 3 • 3D Model=Xi =[X,Y,Z]i T : where i=feature index =1,2…N features. • X can be found by manual measurement • Pose t is the Rotation (R) and Translation (T) of the object at a time t, where t={R3x3,T3x1} t • q t i = [u,v] t i is the image point of the i th 3D feature at time t Xi=1=[102,18,23]T X Y Z Xi=2=[92,126,209]T u= horizontal image position, v=vertical image position Pose estimation V0.a
Intro) Motivation I Pose est. I Newton's method I Iterative method What is Structure from motion sem? 3D Model=X;: where i=feature index =1, 2.N features t=3 Time(t) 41=N t=T i=N t=1 2 R 3×313×1t=2 (R3 (R3 3×313×1)t=3 (R33,I,x1 3×313×1t=1 Capture images at time index t=1, 2, Extract image features qi, i=feature index =12, 3.N To Find: Pose at timet is(R3x37I3xI) and structure of the object(X,Y, Z of each 3-D feature on the object) 4 Pese-estimatien Oa
Intro. | Motivation | Pose est.| Newton’s method | Iterative method What is Structure From Motion SFM? • 3D Model=Xi : where i=feature index =1,2…N features 4 t=1 t= 2 t=3 … Time (t) 3 3 3 1 1 ( , ) R T t= structure of the object (X,Y,Z of each 3- D feature on the object) To Find :Pose at time is , and Extract image features feature index 12 3 Capture images at time index 1 2 3 3 3 1 t t i t (R T ) q ,i , ..N t , ,...Γ = = = 1 2 = = t i q 1 1 = = t i q =1 = t i N q = = t qi N 3 3 3 1 2 ( , ) R T t= 3 3 3 1 3 ( , ) R T t= R T t= ( , ) 3 3 3 1 Pose estimation V0.a
Intro)I Motivation I Pose est. I Newton's method I Iterative method Methods of structure from motion sem: 3D reconstruction from n-frames Factorization(linear, fast, not too accurate) Bundle adjustment ba (slower but more accurate) can use factorization results as the first guess Non-linear iterative methods are more accurate than linear method require first guess(e.g. From factorization) Many different implementations but the concept is the same Two-step Bundle Adjustment(a special form of Bundle adjustment BA) Iterative pose estimation Iterative structure reconstruction Pose estimation vo.a 5
Intro. | Motivation | Pose est.| Newton’s method | Iterative method Methods of Structure From Motion SFM :3D reconstruction from N-frames • Factorization (linear, fast, not too accurate) • Bundle adjustment BA (slower but more accurate), can use factorization results as the first guess. – Non-linear iterative methods are more accurate than linear method, require first guess (e.g. From factorization). – Many different implementations, but the concept is the same. – Two-step Bundle Adjustment (a special form of Bundle adjustment BA) • Iterative pose estimation • Iterative structure reconstruction Pose estimation V0.a 5