MSU CSE 803 Stockman CV: Matching in 2D Matching 2D images to 2D images; Matching 2D images to 2D maps or 2D models; Matching 2D maps to 2D maps

MSU CSE 803 Stockman 2D Matching Problem 1) Need to match images to maps or models 2) need to match images to images Applications 1) land use inventory matches images to maps 2) object recognition matches images to models 3) comparing X-rays before and after surgery

MSU CSE 803 Stockman Methods for study Recognition by alignment Pose clustering Geometric hashing Local focus feature Relational matching Interpretation tree Discrete relaxation

MSU CSE 803 Stockman Tools and methods Algebra of affine transformations scaling, rotation, translation, shear Least-squares fitting Nonlinear warping General algorithms graph-matching, pose clustering, discrete relaxation, interpretation tree

MSU CSE 803 Stockman Alignment or registration DEF: Image registration is the process by which points of two images from similar viewpoints of essentially the same scene are geometrically transformed so that corresponding features of the two images have the same coordinates

MSU CSE 803 Stockman x y u v

11 matching control points x, y, u, v below = T [ u, v, 1] = T [x, y, 1] t

MSU CSE 803 Stockman Least Squares in MATLAB BigPic = LilPic = [ a11 a21 a12 a22 = a13 a23 ]

MSU CSE 803 Stockman Least squares in MATLAB 2 >> AFFINE = BigPic \ LilPic AFFINE = >> ERROR = LilPic - BigPic * AFFINE ERROR = Worst is 1.8 pixels The solution is such that the 11D vector at the right has the smallest L2 norm

MSU CSE 803 Stockman Least squares in MATLAB 3 X = >> Y Y = >> T = X \ Y T = >> E = Y - X*T E = Solution from 4 points has smaller error on those points

MSU CSE 803 Stockman Least squares in MATLAB 4 When the affine transformation obtained from 4 matching points is applied to all 11 points, the error is much worse than when the transformation was obtained from those 11 points. >> E2 = LilPic - BigPic * T E2 =

MSU CSE 803 Stockman Components of transformations Scaling, rotation, translation, shear

MSU CSE 803 Stockman scaling transformation

MSU CSE 803 Stockman Rotation transformation

MSU CSE 803 Stockman Pure rotation

MSU CSE 803 Stockman Orthogonal tranformations DEF: set of vectors is orthogonal if all pairs are perpendicular DEF: set of vectors is orthonormal if it is orthogonal and all vectors have unit length Orthogonal transformations preserve angles Orthonormal transformations preserve angles and distances Rotations and translations are orthonormal DEF: a rigid transformation is combined rotation and translation

MSU CSE 803 Stockman Translation requires homogeneous coordinates

MSU CSE 803 Stockman Rotation, scaling, translation

MSU CSE 803 Stockman Model of shear

MSU CSE 803 Stockman General affine transformation

MSU CSE 803 Stockman Solving for an RST using control points

MSU CSE 803 Stockman Extracting a subimage by subsampling

MSU CSE 803 Stockman Subsampling transformation

MSU CSE 803 Stockman subsampling At MSU, even the pigs are smart.

MSU CSE 803 Stockman recognition by alignment Automatically match some salient points Derive a transformation based on the matching points Verify or refute the match using other feature points If verified, then registration is done, else try another set of matching points

MSU CSE 803 Stockman Recognition by alignment

MSU CSE 803 Stockman Feature points and distances

MSU CSE 803 Stockman Image features pts and distances

MSU CSE 803 Stockman Point matches reflect distances

MSU CSE 803 Stockman Once matching bases fixed can find any other feature point in terms of the matching transformation can go back into image to explore for the holes that were missed (C and D) can determine grip points for a pick and place robot ( transform R and Q into the image coordinates)

MSU CSE 803 Stockman Compute transformation Once we have matching control points (H2, A) and (H3, B) we can compute a rigid transform

MSU CSE 803 Stockman Get rotation easily, then translation

MSU CSE 803 Stockman Generalized Hough transform Cluster evidence in transform parameter space

MSU CSE 803 Stockman See plastic slides matching maps to images

MSU CSE 803 Stockman “Best” affine transformation from overdetermined matches

MSU CSE 803 Stockman “Best” affine transformaiton Use as many matching pairs ((x,y)(u,v)) as possible

MSU CSE 803 Stockman result for previous town match