Registration Techniques
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1 EMBO Practical Course on Light Sheet Microscopy Junior-Prof. Dr. Olaf Ronneberger Computer Science Department and BIOSS Centre for Biological Signalling Studies University of Freiburg Germany O. Ronneberger, Uni Freiburg / / slide 1
2 Motivation Registration, that you have seen so far (in Stephans talk this morning) All images taken from the same individual Feature-based registration using point-to-point correspondences (bead or nuclei positions) Rigid/Affine transformation What I will show Images from different individuals Mainly intensity-based registration Elastic transformation O. Ronneberger, Uni Freiburg / / slide 2
3 Elastic Registration Map Patterns from Many Individuals to a Common Atlas O. Ronneberger, K. Liu, M. Rath, D. Rueß, T. Mueller, H. Skibbe, B. Drayer, T. Schmidt, A. Filippi, R. Nitschke, T. Brox, H. Burkhardt, W. Driever: ViBE-Z: A Framework for 3D Virtual Colocalization Analysis in Zebrafish Larval Brains. Nature Methods, 9(7): , 2012 O. Ronneberger, Uni Freiburg / / slide 3
4 Virtual Colocalization Studies O. Ronneberger, Uni Freiburg / / slide 4
5 Manual Segmentation of Reference Brain O. Ronneberger, Uni Freiburg / / slide 5
6 Automated Anatomical Assignment O. Ronneberger, Uni Freiburg / / slide 6
7 Automated Anatomical Assignment O. Ronneberger, Uni Freiburg / / slide 7
8 Elastic Registration Use the anatomy channel to find the transformation Use found transformation to transform the pattern channel New Recording T Anatomy channel Reference (Atlas) Anatomy channel T Pattern channel Pattern channel (aligned to atlas) O. Ronneberger, Uni Freiburg / / slide 8
9 Registration Definition: Bring two images into spatial alignment Fixed image Moving Image Output More technical: One fixed image and one moving image Find optimal transformation parameters, such that the moving image matches best the fixed image Output: Transformation parameters Transformed moving image O. Ronneberger, Uni Freiburg / / slide 9
10 Registration Categories Feature based Registration Fixed image Moving Image use manually or automatically detected landmarks compute transformation, such that moving and fixed landmarks are placed onto each other right eye left eye Fixed image I ma g n i v o M ge Intensity based Registration Iteratively transform moving image and compare image intensities to find optimal alignment O. Ronneberger, Uni Freiburg / / slide 10
11 Landmark Based Registration moving image fixed image Rigid transformation: minimize the squared distance between corresponding landmarks O. Ronneberger, Uni Freiburg / / slide 11
12 Landmark Based Registration moving image fixed image Elastic Transformation (here Thin-plate Splines): deform image, such that landmarks match exactly O. Ronneberger, Uni Freiburg / / slide 12
13 Thin-Plate Splines (TPS) Example new larva with landmarks reference larva with landmarks O. Ronneberger, Uni Freiburg / / slide 13
14 Raw Overlay 100µm Central slice. magenta: reference larva, green: new larva O. Ronneberger, Uni Freiburg / / slide 14
15 After Landmark-Based Elastic Registration 100µm For images from different individuals, we can not do much better: - usually only a few point-to-point correspondences are available! Central slice. magenta: reference larva, green: new larva O. Ronneberger, Uni Freiburg / / slide 15
16 After Intensity Based Elastic Registration 100µm Central slice. magenta: reference larva, green: new larva only brain region is considered O. Ronneberger, Uni Freiburg / / slide 16
17 Intensity based Registration How does a human register two images? Fixed image Moving Image on transparent slide O. Ronneberger, Uni Freiburg / / slide 17
18 O. Ronneberger, Uni Freiburg / / slide 18
19 O. Ronneberger, Uni Freiburg / / slide 19
20 O. Ronneberger, Uni Freiburg / / slide 20
21 O. Ronneberger, Uni Freiburg / / slide 21
22 O. Ronneberger, Uni Freiburg / / slide 22
23 O. Ronneberger, Uni Freiburg / / slide 23
24 O. Ronneberger, Uni Freiburg / / slide 24
25 Parts of a Registration Algorithm How does a human register two images? Fixed image Moving Image on transparent slide Final registration O. Ronneberger, Uni Freiburg / / slide 25
26 General Flow Chart for a Registration Fixed image Compute Similarity Moving image Similarity score Optimizer Transformation transformed Moving image Improved Transformation parameters O. Ronneberger, Uni Freiburg / / slide 26
27 The 3 Parts of a Registration Algorithm A transformation model What can you do with the moving image. e.g. rigid transformation (corresponds to our slide) or elastic transformation (put moving image on a rubber skin) A similarity measure Compare the gray values of fixed and moving image and output a score An optimizer Algorithm to find the transformation parameters O. Ronneberger, Uni Freiburg / / slide 27
28 Component 1: The Transformation Fixed image Compute Similarity Moving image Similarity score Optimizer Transformation transformed Moving image Improved Transformation parameters O. Ronneberger, Uni Freiburg / / slide 28
29 Typical Transformation Models Translation only 2D images: 2 parameters (shift in x and shift in y direction, denoted as u,v) 3D images: 3 parameters (shift in x, y, and z direction) Rigid Transformation (shift and rotation) 2D images: 3 parameters (shift x, shift y, rotation angle) 3D images: 6 parameters (shift x, y, and z, rotation around x-, y- and z-axis) O. Ronneberger, Uni Freiburg / / slide 29
30 Typical Transformation Models Affine Transformation (shift, rotation, scale and skew) 2D images: 6 parameters 3D images: 12 parameters Elastic Registration 2D images: 2 times the number of pixels 3D images: 3 times the number of voxels O. Ronneberger, Uni Freiburg / / slide 30
31 Component 2: The Similarity Measure Fixed image Compute Similarity Moving image Similarity score Optimizer Transformation transformed Moving image Improved Transformation parameters O. Ronneberger, Uni Freiburg / / slide 31
32 Similarity Measures Case 1: Identical Gray Values e.g., transmitted light images of moving cells O. Ronneberger, Uni Freiburg / / slide 32
33 Similarity Measures for Intensity Based Registration a0 b0 Image A Image B O. Ronneberger, Uni Freiburg / / slide 33
34 Similarity Measures for Intensity Based Registration a1 b1 Image A Image B O. Ronneberger, Uni Freiburg / / slide 34
35 Similarity Measures for Intensity Based Registration a2 Image A b2 Image B O. Ronneberger, Uni Freiburg / / slide 35
36 Similarity Measures Case 1: Identical Gray Values Sum of Squared Differences (SSD) Compute squared difference between intensity of each pixel ai in the fixed image and intensity of the corresponding pixel bi in the transformed moving image Sum up for all pixels Standard Error model (assumes Gaussian distribution of errors) Allows effective optimization in certain algorithms O. Ronneberger, Uni Freiburg / / slide 36
37 Similarity Measures Case 1: Identical Gray Values Sum of Absolute Differences (SAD) Compute absolute difference between intensity of each pixel ai in the fixed image and intensity of the corresponding pixel bi in the transformed moving image Sum up for all pixels Less sensitive to outlier intensities than SSD Both methods only for images recorded under identical conditions! O. Ronneberger, Uni Freiburg / / slide 37
38 Similarity Measures Case 2: Gray Value Offset and Scale µm 4µm e.g. fluorescent cells, over time with bleaching O. Ronneberger, Uni Freiburg / / slide 38
39 Similarity Measures Case 2: Gray Value Offset and Scale Normalized Cross Correlation Subtract the mean value of each image Compute the product of each pixel ai in the fixed image and the corresponding pixel bi in the transformed moving image and sum up for all pixels Normalize with standard deviation of each Image standard deviation of intensities mean value of intensities different intensity offsets (e.g. background intensities) are compensated different intensity scales (contrast changes) are compensated Extension: Compute mean and stddev only in a local surrounding: High robustness, even for very different contrast within the same image! O. Ronneberger, Uni Freiburg / / slide 39
40 Similarity Measures Case 3: Different Modalities e.g. CT scan (X-Ray) and MRI scan (Magnetic Resonance) O. Ronneberger, Uni Freiburg / / slide 40
41 Similarity Measures Case 3: Different Modalities Mutual Information Standard measure in medical image registration, when registering images from different modalities (e.g. CT and MRI) Allows any dependencies of intensities in the images (e.g. bones are white in CT and black in MRI) (we don't go into detail here) O. Ronneberger, Uni Freiburg / / slide 41
42 Component 3: The Optimizer Fixed image Compute Similarity Moving image Similarity score Optimizer Transformation transformed Moving image Improved Transformation parameters O. Ronneberger, Uni Freiburg / / slide 42
43 The Optimizier searches the best Parameters. Intuitive visualisation of optimizer by drawing the similarity measure as function of the parameters For two parameters, you can think of mountains. Your job is to find the peak. But you are blind, you can explore the surrounding by feeling with your feet Similiarity measure Optimiziers pa r am ete r1 p er t e ar am 2 O. Ronneberger, Uni Freiburg / / slide 43
44 Best Neighbor Optimizer 1. Evaluate all 2n neighbors of the current location 2. If better than the current value, set best neighbor as next location, repeat Otherwise half the step size and try again 4. Abort if step size or cost function difference below limit Slow, but works very stable only locations are chosen that have been evaluated O. Ronneberger, Uni Freiburg / / slide 44
45 Gradient Descent Optimizer If you can compute the gradient at your current position 1. determine gradient (that is, in with direction the mountain raises) 2. go as far in that direction, until it does not increase anymore 3. repeat steps 1,2 until convergence O. Ronneberger, Uni Freiburg / / slide 45
46 Problem of these optimizers Do you see the problem of all these optimizers? Similiarity measure Local maxima pa ra me ter 1 er t e m para 2 O. Ronneberger, Uni Freiburg / / slide 46
47 Higher Dimensional Parameter Spaces In reality there are usually much more than only 2 parameters (like in the mountain metaphor) Metaphor for 3 parameters: You dive in the ocean, and you have to find the warmest spot. [image from wikipedia: Taucher ] O. Ronneberger, Uni Freiburg / / slide 47
48 Put all together for 2D smiley registration matlab demo: O. Ronneberger, Uni Freiburg / / slide 48
49 Elastic Registration Fixed image I Moving Image J Transformation T O. Ronneberger, Uni Freiburg / / slide 49
50 Smoothness Term Transformation is described by a vector field (individual displacement vector for each voxel) Not all vector fields describe reasonable deformations Neighboring points should have similar displacement We need a regularization, that enforces a smooth deformation Very important: Optimize smoothness and image similarity simultaneously! Many available software packages do this wrong. O. Ronneberger, Uni Freiburg / / slide 50
51 Elastic Registration Flow Diagram fixed image I Compute Similarity Apply Transformation Energy transformed moving image J' moving image J Compute Smoothness Optimizer λ weight for smoothness term Transformation T O. Ronneberger, Uni Freiburg / / slide 51
52 Problem with Gradient-based Optimization Standard approach: Optimize per position 1 continuous variable (3 comp) - runs into best direction Combinatorial approach: Optimize per position N binary variables (with constraint: sum=1) - checks many hypotheses Problem: In 3D not possible to store all these variables for each voxel: Number of voxels times number of displacement hypotheses Use grid based registration to reduce number of variables. O. Ronneberger, Uni Freiburg / / slide 52
53 Control Point Grid O. Ronneberger, Uni Freiburg / / slide 53
54 Combinatorial Optimization Discretization: Regular grid of control points (nodes) At each control point discrete number of displacement hypotheses (labels) Data term unary term: similarity measure of fixed image (red patch) and moving image (green patch) for the given displacement Smoothness term pairwise term: difference of two neighboring displacement vectors O. Ronneberger, Uni Freiburg / / slide 54
55 Dense displacement field O. Ronneberger, Uni Freiburg / / slide 55
56 Landmark-Based Pre-Registration 100µm Central slice. magenta: reference larva, green: new larva O. Ronneberger, Uni Freiburg / / slide 56
57 After Intensity Based Elastic Registration 100µm Central slice. magenta: reference larva, green: new larva only brain region is considered O. Ronneberger, Uni Freiburg / / slide 57
58 Results Use FastPD solver for combinatorial optimization (Komodakis et al. 2008) Primal-Dual strategy, updates use fast graph-cut algorithm Very fast algorithm. In zebrafish setup solver only takes a few seconds. Most time is spent on computing the cross-correlations Only two iterations needed Overall computation time approx. 3 minutes on a 6core Xeon dataset with 1000x500x500 voxels (3.6 million voxels after downscaling and masking) Nikos Komodakis, Georgios Tziritas, and Nikos Paragios. Performance vs computational efficiency for optimizing single and dynamic mrfs: Setting the state of the art with primal-dual strategies. Comput. Vis. Image Underst., 112:14 29, October O. Ronneberger, Uni Freiburg / / slide 58
59 Limitations Only binary potentials possible i.e. in current implementation rotation is more expensive than shear Problem becomes non-submodular from second iteration on (i.e. same label on neighbouring control points has not a pairwise energy zero) work-around used by Glocker et al: fluid-like registration... More complex smoothness terms make problem non-submodular also in first iteration Solution: Don't use FastPD (with graph cuts), but alpha expansion with QPBO --> much slower. O. Ronneberger, Uni Freiburg / / slide 59
60 Conclusions Alignment of different individuals needs intensity-based registration with elastic transformation Combinatorial optimization makes elastic registration less susceptible for local optima. Building block for many further image analysis applications You can try the vibez_elastic_registration on saturday or sunday afternoon Thanks to Pavel, Jan, Jan, Lars and Emmanuel for organizing this great event Thank you for your attention. O. Ronneberger, Uni Freiburg / / slide 60
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