Computer Vision I - Image Matching and Image Formation
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1 Computer Vision I - Image Matching and Image Formation Carsten Rother 10/12/2014 Computer Vision I: Image Formation Process
2 Computer Vision I: Image Formation Process 10/12/ Roadmap for next five lecture Appearance based matching (sec. 4.1) How do we get an RGB image? (sec ) The Human eye The Camera and Image formation model Projective Geometry - Basics (sec ) Geometry of a single camera (sec 2.1.5, 2.1.6) Pinhole camera Lens effects Geometry of two cameras (sec. 7.2) Robust Geometry estimation for two cameras (sec ) Multi-View 3D reconstruction (sec )
3 Matching two Images Computer Vision I: Image Formation Process 10/12/ Find interest points Find orientated patches around interest points to capture appearance Encode patch appearance in a descriptor Find matching patches according to appearance (similar descriptors) Verify matching patches according to geometry (later lecture) v
4 Examples: Appearance-based matching Computer Vision I: Image Formation Process 10/12/2014 4
5 Applications Computer Vision I: Image Formation Process 10/12/ D reconstruction: Augmented Realty: Panoramic Stitching:
6 Roadmap: matching two Images (appearance & geometry) Computer Vision I: Image Formation Process 10/12/ Find interest points Find orientated patches around interest points to capture appearance Encode patch appearance in a descriptor Find matching patches according to appearance (similar descriptors) Verify matching patches according to geometry (later lecture!) v
7 Reminder Lecture 3: Harris Corner Detector Computer Vision I: Image Formation Process 10/12/ Compute: 1. Idea was a so-called auto-correlation function: Harris measure: 4. Take those points (after non-may suppression) with high H value
8 Roadmap: matching two Images (appearance & geometry) Computer Vision I: Image Formation Process 10/12/ Find interest points Find orientated patches around interest points to capture appearance Encode patch appearance in a descriptor Find matching patches according to appearance (similar descriptors) Verify matching patches according to geometry (later lecture) v
9 How to deal with orientation Computer Vision I: Image Formation Process 10/12/ Orientate with image gradient:
10 Choose a patch around each point Computer Vision I: Image Formation Process 10/12/ How to deal with scale?
11 Choose a patch around each point Computer Vision I: Image Formation Process 10/12/ How to deal with scale?
12 Choose a patch around each point Computer Vision I: Image Formation Process 10/12/ How to deal with scale?
13 Reminder: Edge detection via image gradient Computer Vision I: Image Formation Process 10/12/ Image gradient: ( (D x G) I, (D y G) I) Image Result of (using small sigma) Result of (using large sigma) Final result with canny edge detector
14 Alterative Edge Detector via LoG Operator Computer Vision I: Image Formation Process 10/12/ To find an edge we first smooth is called the LoG (Laplacian of Gaussian operator) 1D example: 2D example (Mexican hat): Find zero-crossing
15 Alterative: Edge detection with LoG Filter Computer Vision I: Image Formation Process 10/12/ Called Laplacian of Gaussian (LoG)
16 Scale selection (illustration) Computer Vision I: Image Formation Process 10/12/ f is Laplacian of Gaussian (LoG) operator. Measures an average edge-ness in all directions 2 G(σ) I = 2 (G(σ) I) x (G(σ) I) y 2 (details on page 191)
17 Scale selection (illustration) Computer Vision I: Image Formation Process 10/12/
18 Scale selection (illustration) Computer Vision I: Image Formation Process 10/12/
19 Scale selection (illustration) Computer Vision I: Image Formation Process 10/12/
20 Scale selection (illustration) Computer Vision I: Image Formation Process 10/12/ We could match up these curves and find unique corresponding points
21 Scale selection (illustration) Computer Vision I: Image Formation Process 10/12/ Simpler: Find maxima / minima in the curves, respectively
22 Roadmap: matching 2 Images (appearance & geometry) Computer Vision I: Image Formation Process 10/12/ Find interest points Find orientated patches around interest points to capture appearance Encode patch appearance in a descriptor Find matching patches according to appearance (similar descriptors) Verify matching patches according to geometry v
23 SIFT feature 64 pixels Computer Vision I: Image Formation Process 10/12/ v 64 pixels 4*4=16 cells Each cell has an 8 bin histogram (smoothed across cells) In total: 16*8 values, i.e. 128D vector A cell has 16x16 pixels (here 8x8 for illustration only) (blue circle shows center weighting) [Lowe 2004]
24 SIFT feature is very popular Computer Vision I: Image Formation Process 10/12/ Fast to compute Can handle large changes in viewpoint well (up to 60 o out of plane rotation) Can handle photometric changes (even day versus night)
25 Many other feature descriptors Computer Vision I: Image Formation Process 10/12/ MOPS [Brown, Szeliski and Winder 2005] SURF [Herbert Bay et al. 2006] DAISY [Tola, Lepetit, Fua 2010] Shape Context. DAISY
26 Roadmap: matching 2 Images (appearance & geometry) Computer Vision I: Image Formation Process 10/12/ Find interest points Find orientated patches around interest points to capture appearance Encode patch appearance in a descriptor Find matching patches according to appearance (similar descriptors) Verify matching patches according to geometry (later lecture) v
27 Find matching patches fast Computer Vision I: Image Formation Process 10/12/ N patches (e.g. N = 1000) N patches (e.g. N = 1000) Goal: 1) Find for each patch in left image the closest in right image 2) Accept all those matches where descriptors are similar enough Methods: Naïve: N 2 tests (here 1 Million) Hashing Hashing (not discussed) Kd-tree; on average NlogN tests (here ~10,000) (Hashing Function) Index for patch DB
28 Subtask: Find one patch Computer Vision I: Image Formation Process 10/12/ Query patch? Database image
29 Nearest Neighbor Search Computer Vision I: Image Formation Process 10/12/ Tracking in Video The video is the Database Image retrieval Whole image has one descriptor Database is an image collection
30 Kd-tree (d stands for dimension) Computer Vision I: Image Formation Process 10/12/ Build the tree over database image: 1) Cycle over dimensions: x,y,z,x,y,z,. 2) Put in axis-aligned hyper-planes (split at median of point set) Example in 3D Result: balanced tree Nearest Neighbour search (to come) [Invented by Jon Louis Bentley 1975]
31 Examples Computer Vision I: Image Formation Process 10/12/
32 Dimension 2 Examples Computer Vision I: Image Formation Process 10/12/ Kd-tree d1>5 2 1,2,3 4,5, Dimension 1
33 Dimension 2 Examples Computer Vision I: Image Formation Process 10/12/ Kd-tree d1>5 2 d2>4.8 d2> ,3 5 4, Dimension 1
34 Dimension 2 Examples Computer Vision I: Image Formation Process 10/12/ Kd-tree d1>5 2 d2>4.8 d2> d1>1 5 d1> Dimension
35 Dimension 2 Examples: nearest neighbor search Computer Vision I: Image Formation Process 10/12/ Kd-tree d1>5 2 d2>4.8 d2> query 1 d1>1 5 d1> Dimension
36 Dimension 2 Examples: nearest neighbor search Computer Vision I: Image Formation Process 10/12/ Kd-tree d1>5 2 d2>4.8 d2>6.5 4 search radius 5 1 query 1 d1>1 5 d1> Dimension 1 find leave where query is in visited current best
37 Dimension 2 Examples: nearest neighbor search Computer Vision I: Image Formation Process 10/12/ Kd-tree d1>5 Radius not intersected 2 d2>4.8 d2>6.5 4 search radius 5 1 query 1 d1>1 5 d1> Dimension visited current best
38 Dimension 2 Computer Vision I: Image Formation Process 10/12/ Examples: nearest neighbor search search radius query 6 Radius intersects. Go down this subtree and find in all touching pockets (here one) the closest point. Take it as new candidate if closer than d2>4.8 current one 1 Kd-tree d1>1 d1>5 5 d2>6.5 d1> Dimension visited current best
39 Dimension 2 Examples: nearest neighbor search Computer Vision I: Image Formation Process 10/12/ Kd-tree d1>5 2 d2>4.8 d2>6.5 4 search radius 1 5 query better solution found 1 d1>1 5 d1> Dimension visited current best
40 Dimension 2 Examples: nearest neighbor search Computer Vision I: Image Formation Process 10/12/ Kd-tree d1>5 2 d2>4.8 d2>6.5 4 search radius 5 1 query 1 d1>1 5 d1> Dimension 1 no need to visit these subtrees visited current best
41 Dimension 2 Examples: nearest neighbor search Computer Vision I: Image Formation Process 10/12/ Kd-tree d1>5 2 d2>4.8 d2>6.5 4 search radius 5 1 query 1 d1>1 5 d1> Dimension Done since root-node is marked in both ways visited current best
42 Nearest neighbour search pseudo code Computer Vision I: Image Formation Process 10/12/ Input: query point Step 1: Find leave node (bucket) with query point Step 2: Make hyper-sphere with radius (current best and query point) Step3: go up the tree and see if hyper-plane intersects hyper-sphere Step 3a: no intersection: mark tree branch as visited since no better point can be found there. Step 3b: intersection: If not yet marked as visited, then go down the other branch to find potentially a better point (in all touching pockets). If so, mark as current best and go to Step 2, otherwise mark as visited. Stop criteria: root node has both branches marked as visited. On average O(log N) Pseudo code Nothing better possible Hyper-plane positions Current best query
43 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/ From Andrew Moore:
44 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
45 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
46 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
47 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
48 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
49 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
50 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
51 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
52 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
53 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
54 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
55 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
56 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
57 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
58 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
59 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
60 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
61 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
62 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
63 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
64 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
65 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
66 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
67 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
68 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
69 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
70 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
71 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
72 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
73 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
74 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
75 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/
76 Example with many points in 2D Computer Vision I: Image Formation Process 10/12/ done
77 Roadmap: matching 2 Images (appearance & geometry) Computer Vision I: Image Formation Process 10/12/ Find interest points (including different scales) Find orientated patches around interest points to capture appearance Encode patch in a descriptor Find matching patches according to appearance (similar descriptors) Verify matching patches according to geometry (later lecture) v
78 Halfway Computer Vision I: Image Formation Process 10/12/ Minutes Break Question?
79 Roadmap for next five lecture Computer Vision I: Image Formation Process 10/12/ Appearance based matching (sec. 4.1) How do we get an RGB image? (sec ) The Human eye The Camera and Image formation model Projective Geometry - Basics (sec ) Geometry of a single camera (sec 2.1.5, 2.1.6) Pinhole camera Lens effects Geometry of two cameras (sec. 7.2) Robust Geometry estimation for two cameras (sec ) Multi-View 3D reconstruction (sec )
80 Computer Vision I: Image Formation Process 10/12/ The Human eye The retina contains different types of sensors: cones Zapfen (colors, 6 million) and rods Stäbchen (gray levels, 120 million) The resolution is much higher in fovea centralis Light first passes through the layer of neurons before it reaches photo sensors (smoothing). Only in the fovea centralis the light hits directly the photo sensors Signal goes out the other way: Retina Ganglion cells (1 million) Optic nerve 1 MPixel Camera?
81 Spatial resolution Computer Vision I: Image Formation Process 10/12/
82 Spatial resolution 2MP Camera, far from the screen. Image Processing: Human seeing 5
83 Spatial resolution 5MP Camera, close to the screen. Image Processing: Human seeing 5
84 Spatial resolution (secrets) Computer Vision I: Image Formation Process 10/12/ The resolution is much higher In fovea centralis The Information is pre-processed by Ganglion cells (Compare: =7MPixel, 2.4 MB RGB JPEG lossless) No still image, but a Video (super-resolution) Scanning technique Saccades
85 Eye Saccades Computer Vision I: Image Formation Process 10/12/ Eyes never move uniformly, but jump in saccades (approximately ms duration between fixation points) Saccades are driven by the importance of the scene parts (eyes, mouth etc).
86 The Human eye Computer Vision I: Image Formation Process 10/12/ cones Zapfen What is light? Spectrum, i.e. a function of the wavelength Different colors can be computed by adding /subtracting signal of rods Spectral resolution of the eye is relatively bad due to projection
87 Computer Vision I: Image Formation Process 10/12/ Roadmap for next five lecture Appearance based matching (sec. 4.1) How do we get an RGB image? (sec ) The Human eye The Camera and Image formation model Projective Geometry - Basics (sec ) Geometry of a single camera (sec 2.1.5, 2.1.6) Pinhole camera Lens effects Geometry of two cameras (sec. 7.2) Robust Geometry estimation for two cameras (sec ) Multi-View 3D reconstruction (sec )
88 Image formation Process Computer Vision I: Image Formation Process 10/12/
89 Model of the Surface Computer Vision I: Image Formation Process 10/12/ BRDF (Bi-directional Reflectance Function) light x ω i ω o Rendering equation: Incoming energy (shining surface) Incoming light Outgoing energy: BRDF function t: time (4DoF only ω i, ω o x position considered) λ: wavelength ω i /ω o : incoming/outgoing direction Fore-shorting angle (always 0)
90 Computer Vision I: Image Formation Process 10/12/ Example: diffuse reflectance (also known as the Lambertian world assumption ) Rendering equation DIFFUSE 0 constant f r same for all ω o Single Light source: 0 constant Shading effects come from: max(0, w i n) constant (one ω i )
91 Computer Vision I: Image Formation Process 10/12/ Examples: BRDFs Rendering equation (single light source) 0 constant (one ω i ) DIFFUSE SPECULAR DIFFUSE + ROUGH SPECULAR f f r f r r (for one ω i and all ω o ) (for one ω i and all ω o ) (for one ω i and all ω o ) Single light source (from top; right)
92 Inside a graphics engine Computer Vision I: Image Formation Process 10/12/ Rendering equation Ray tracing Radiosity
93 Example Computer Vision I: Image Formation Process 10/12/ Texture only 3D scene in blender Direct light Global lighting (direct + indirect)
94 Capturig BRDF / BTF capture Computer Vision I: Image Formation Process 10/12/ BTF Bidirectional Texture function. At every spatial location x a different BRDF [Christopher Schwartz, Ralf Sarlette, Michael Weinmann and Reinhard Klein]
95 Camera types Computer Vision I: Image Formation Process 10/12/ RGB cameras Depth cameras: Passive RGB stereo Active Structured Light stereo Active Time of Flight Lightfield cameras
96 Digital RGB cameras Computer Vision I: Image Formation Process 10/12/ A digital camera replaces film with a sensor array Each cell in the sensor array is light-sensitive diode that converts photons to electrons Two common types: Charge Coupled Device (CCD) Complementary metal oxide semiconductor (CMOS)
97 Color - Filters Computer Vision I: Image Formation Process 10/12/
98 Problem with de-mosaicing: color moiré Computer Vision I: Image Formation Process 10/12/
99 Cause of color moiré Computer Vision I: Image Formation Process 10/12/
100 There is a lot of image processing in camera Computer Vision I: Image Formation Process 10/12/ Image taken zoom
101 In-camera processing Computer Vision I: Image Formation Process 10/12/
102 Depth camera: Time of Flight Computer Vision I: Image Formation Process 10/12/ Intensity image Depth Image PMD Camera Sends out infra-red light and looks at changes in phase and magnitude
103 Depth Camera passive RGB stereo Computer Vision I: Image Formation Process 10/12/ Easy to match hard to match
104 Depth Camera Structured Light Computer Vision I: Image Formation Process 10/12/ perform matching (as with passive stereo camera) but now with a nicely textured image Only works well when external Infre-red light is not too strong (e.g. not with sunlight)
105 Lightfield cameras Computer Vision I: Image Formation Process 10/12/ Capture all light: Refocus and change perspective with one image
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