Prof. Feng Liu. Spring /26/2017
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1 Prof. Feng Liu Spring /26/2017
2 Last Time Re-lighting HDR 2
3 Today Panorama Overview Feature detection Mid-term project presentation Not real mid-term 6 minutes presentation Schedule May 8 and 10 With slides by Prof. C. Dyer and K. Grauman 3
4 Panorama Building: History Along the River During Ching Ming Festival by Z.D Zhang ( ) San Francisco from Rincon Hill, 1851, by Martin Behrmanx 4
5 Panorama Building: A Concise History The state of the art and practice is good at assembling images into panoramas Mid 90s Commercial Players (e.g. QuicktimeVR) Late 90s Robust stitchers(in research) Early 00s Consumer stitching common Mid 00s Automation 5
6 Stitching Recipe Align pairs of images Align all to a common frame Adjust (Global) & Blend 6
7 Stitching Images Together 7
8 When do two images stitch? 8
9 Images can be transformed to match 9
10 Images are related by Homographies 10
11 Compute Homographies 11
12 Automatic Feature Points Matching Match local neighborhoods around points Use descriptors to efficiently compare SIFT [Lowe 04] most common choice 12
13 Stitching Recipe Align pairs of images Align all to a common frame Adjust (Global) & Blend 13
14 Wide Baseline Matching Images taken by cameras that are far apart make the correspondence problem very difficult Feature-based approach: Detect and match feature points in pairs of images
15 Matching with Features Detect feature points Find corresponding pairs
16 Matching with Features Problem 1: Detect the same point independently in both images no chance to match! We need a repeatable detector
17 Matching with Features Problem 2: For each point correctly recognize the corresponding point? We need a reliable and distinctive descriptor
18 Properties of an Ideal Feature Local: features are local, so robust to occlusion and clutter (no prior segmentation) Invariant (or covariant) to many kinds of geometric and photometric transformations Robust: noise, blur, discretization, compression, etc. do not have a big impact on the feature Distinctive: individual features can be matched to a large database of objects Quantity: many features can be generated for even small objects Accurate: precise localization Efficient: close to real-time performance
19 Problem 1: Detecting Good Feature Points [Image from T. Tuytelaars ECCV 2006 tutorial]
20 Feature Detectors Hessian Harris Lowe: SIFT (DoG) Mikolajczyk & Schmid: Hessian/Harris-Laplacian/Affine Tuytelaars & Van Gool: EBR and IBR Matas: MSER Kadir & Brady: Salient Regions Others
21 Harris Corner Point Detector C. Harris, M. Stephens, A Combined Corner and Edge Detector, 1988
22 Harris Detector: Basic Idea We should recognize the point by looking through a small window Shifting a window in any direction should give a large change in response
23 Harris Detector: Basic Idea flat region: no change in all directions edge : no change along the edge direction corner : significant change in all directions
24 Harris Detector: Derivation Change of intensity for a (small) shift by [u,v] in image I: xy, 2 E( u, v) w( x, y) I( x u, y v) I( x, y) Weighting function Shifted intensity Intensity Weighting function w(x,y) = or 1 in window, 0 outside Gaussian Credit: R. Szeliski
25 Apply 2 nd order Taylor series expansion: y x y x y x y y x x y x I y x I y x w C y x I y x w B y x I y x w A Bv Cuv Au v u E,, 2, ), ( ), ( ), ( ), ( ), ( ), ( ), ( 2 ), ( (, ) A C u E u v u v C B v x y x I I x / ), ( y y x I I y / ), ( Harris Detector Credit: R. Szeliski
26 Harris Corner Detector Expanding E(u,v) in a 2 nd order Taylor series, we have, for small shifts, [u,v], a bilinear approximation: u E( u, v) u, v M v where M is a 2 2 matrix computed from image derivatives: M 2 I x I xi y w( x, y) 2 xy, I xi y I y I x I y I ( x, y) / x I ( x, y) / y Note: Sum computed over small neighborhood around given pixel Credit: R. Szeliski
27 Harris Corner Detector Intensity change in shifting window: eigenvalue analysis u E( u, v) u, v M v 1, 2 eigenvalues of M Ellipse E(u,v) = const direction of the fastest change direction of the slowest change ( max ) -1/2 ( min) -1/2 Credit: R. Szeliski
28 Selecting Good Features Image patch SSD surface 1 and 2 both large
29 Selecting Good Features SSD surface large 1, small 2
30 Selecting Good Features SSD surface small 1, small 2
31 Harris Corner Detector Classification of image points using eigenvalues of M: 2 Edge 2 >> 1 Corner 1 and 2 both large, 1 ~ 2 ; E increases in all directions 1 and 2 are small; E is almost constant in all directions Flat region Edge 1 >> 2 1
32 Harris Corner Detector Measure of corner response: R det M k M trace 2 det M trace M k is an empirically-determined constant; e.g., k = 0.05
33 Harris Corner Detector R depends only on eigenvalues of M 2 Edge R < 0 Corner R is large for a corner R is negative with large magnitude for an edge R > 0 R is small for a flat region Flat R small Edge R < 0 1
34 Harris Corner Detector: Algorithm Algorithm: 1. Find points with large corner response function R (i.e., R > threshold) 2. Take the points of local maxima of R (for localization) by nonmaximum suppression
35 Harris Detector: Example
36 Harris Detector: Example Compute corner response R = 1 2 k( ) 2
37 Harris Detector: Example Find points with large corner response: R > threshold
38 Harris Detector: Example Take only the points of local maxima of R
39 Harris Detector: Example
40 Harris Detector: Example Interest points extracted with Harris (~ 500 points)
41 Harris Detector: Example
42 Harris Detector: Summary Average intensity change in direction [u,v] can be expressed in bilinear form: u E( u, v) u, v M v Describe a point in terms of eigenvalues of M: measure of corner response: R 2 k A good (corner) point should have a large intensity change in all directions, i.e., R should be a large positive value
43 Harris Detector Properties Rotation invariance Ellipse rotates but its shape (i.e., eigenvalues) remains the same Corner response R is invariant to image rotation
44 Harris Detector Properties But not invariant to image scale Fine scale: All points will be classified as edges Coarse scale: Corner
45 Harris Detector Properties Quality of Harris detector for different scale changes Repeatability rate: # correct correspondences # possible correspondences C. Schmid et al., Evaluation of Interest Point Detectors, IJCV 2000
46 Invariant Local Features Goal: Detect the same interest points regardless of image changes due to translation, rotation, scale, viewpoint 46
47 Models of Image Change Geometry Rotation Similarity (rotation + uniform scale) Affine (scale dependent on direction) valid for: orthographic camera, locally planar object Photometry Affine intensity change (I a I + b) 47
48 SIFT Detector [Lowe 04] Difference-of-Gaussian (DoG) is an approximation of the Laplacian-of-Gaussian (LoG) = Lowe, D. G., Distinctive Image Features from Scale-Invariant Keypoints, International Journal of Computer Vision, 60, 2, pp , 2004
49 SIFT Detector
50 SIFT Detector
51 Resample Blur Subtract SIFT Detector Algorithm Summary Detect local maxima in position and scale of squared values of difference-of-gaussian Fit a quadratic to surrounding values for sub-pixel and subscale interpolation Output = list of (x, y, ) points
52 References on Feature Descriptors A performance evaluation of local descriptors, K. Mikolajczyk and C. Schmid, IEEE Trans. PAMI 27(10), 2005 Evaluation of features detectors and descriptors based on 3D objects, P. Moreels and P. Perona, Int. J. Computer Vision 73(3), 2007
53 Next Time Panorama Feature matching 53
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