Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape...
-
Upload
kristopher-nicholson -
Category
Documents
-
view
215 -
download
0
Transcript of Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape...
![Page 1: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/1.jpg)
Paper Reading
Dalong Du
Nov.27, 2009
![Page 2: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/2.jpg)
Papers
• Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08.
• Yan Li, Leon Gu, Takeo Kanade. A Robust Shape Model for Multi-view Car Alignment. CVPR09.
![Page 3: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/3.jpg)
A Generative Shape Regularization Model for Robust Face Alignment
Leon Gu and Takeo Kanade
![Page 4: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/4.jpg)
Outline
• Author Introduction.
• Problem Introduction.
• How to do?
• Discussion.
![Page 5: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/5.jpg)
Outline
• Author Introduction.
• Problem Introduction.
• How to do?
• Discussion.
![Page 6: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/6.jpg)
Author Introduction (1/3)
Leon Gu Takeo Kanade(金出武雄 )
![Page 7: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/7.jpg)
Author Introduction (2/3)
• Leon Gu– Ph.D. candidate in the Computer Science
Department at Carnegie Mellon University, advised by Professor Takeo Kanade.
– His main research interest is in developing robust and efficient algorithms for object recognition. A common thread has been the focus on reasoning the shape of visual objects from noisy, real-world images, where the uncertainties over image appearance and imaging conditions are prevalent.
![Page 8: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/8.jpg)
Author Introduction (3/3)
• Takeo Kanade– Director of the Robotics Institute of Carnegie
Mellon University– Wisdom:像外行一样思考,像专家一样实践
![Page 9: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/9.jpg)
Outline
• Author Introduction.
• Problem Introduction.
• How to do?
• Discussion.
![Page 10: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/10.jpg)
Problem Introduction (1/12)
• Face Q consists of N landmark points:– – The geometry information of Q decouples into
two parts:• A canonical shape S
– b– e.g. Or other
linear or nonlinear methods
• A transformation– θ– e.g. similarity s, R, t Or
Affine or others.
x u b b
θ
![Page 11: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/11.jpg)
Problem Introduction (2/12)
• Probabilistic Formulation– Generic alignment problem
•
Where– Pose space Θ is free– Shape space is constrained
• A solution maximizes the posterior
• A chicken and egg problem– A best solution A max posterior
![Page 12: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/12.jpg)
Problem Introduction (3/12)
• In the Eyes of Computer– On the basis of such “noisy observation”,
how can make the best hypothesis (b, θ) ?
Reflectance,Occlusion,Image blur,…..
Noisy feature map
![Page 13: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/13.jpg)
Deformation
Transformation
Image Likelihood
Problem Introduction (4/12)
• A Generative hierarchical model– Deformation
• The magnitude of deformation is controlled by b.
• The canonical shape S is generated from b
through , a process that could be linear or nonlinear.
– Transformation • The transform could be similarity/affine.
– Image Likelihood• Varies with the type of image local feature
– Profile, local image patch, Haar-like feature… …
![Page 14: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/14.jpg)
Deformation
Transformation
Image Likelihood
Problem Introduction (5/12)
• Baseline Model– Linear Deformation
•
Where– Shape prior , Λ is diagonal.– Isotropic shape noise (Probabilistic PCA)– The average residual variance outside of the subspace
, where N is the number of landmark points, M is the subspace dimension.
• {Φ, μ, σ} are learned from training samples.
22
1
1
2
N
mm MN M
![Page 15: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/15.jpg)
Deformation
Transformation
Image Likelihood
Problem Introduction (6/12)
• Baseline Model– Similarity Transform
•
Where– θ={s, R, t} are scale, Rotation, translation coefficients
respectively.– Diagonal observation noise
» measures the noise level of the observation of n-th landmark point.
» » Σ is also learned from training samples.
n
( ( ), )n Dist T S Y
![Page 16: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/16.jpg)
Deformation
Transformation
Image Likelihood
Problem Introduction (7/12)
• Baseline Model– Observed shape Y is generated from
feature point detector.–
• EM– Q-function:– E-step: compute the statistics that are required to
evaluate Q-function.– M-step: maximize Q-function to find the updated shape
and pose.
( , , | ) ( | , ) ( | )p b S Y p Y S p S b Bayes
log ( , , | ) log ( | , ) log ( | )S S S
p b S Y p Y S p S b
![Page 17: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/17.jpg)
Problem Introduction (8/12)
• Alignment algorithm
![Page 18: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/18.jpg)
Problem Introduction (9/12)
• Problems?– Linear deformation model
• Cannot handle faces of rare shapes (babies, etc)• Cannot handle extreme expressions
– Single candidate position for each feature point• Best position may be the one with second strongest
response– This paper extends the generative framework to
handle• Large face shape deformation including extreme
expressions• Multiple candidate positions for each feature point• Identify outliers, like occluded feature points.
![Page 19: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/19.jpg)
Problem Introduction (10/12)
• Handling Extreme Expressions
![Page 20: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/20.jpg)
Problem Introduction (11/12)
• Handling Large Occlusion
![Page 21: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/21.jpg)
Problem Introduction (12/12)
• Handling Real World Images
![Page 22: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/22.jpg)
Outline
• Author Introduction.
• Problem Introduction.
• How to do?
• Discussion.
![Page 23: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/23.jpg)
How to do? (1/12)
• Face Q consists of N landmark points:– – The geometry information of Q decouples into
two parts:• A canonical shape S• A similarity transformation
– Map S from a common reference
frame to the coordinate plane of
the image I
b
θ
![Page 24: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/24.jpg)
How to do? (2/12)
• Make a mixture of constrained Gaussian– Multiple subspace–
![Page 25: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/25.jpg)
How to do? (3/12)
• Allow generate multiple candidate– For n-th landmark
• K candidate positions • denote the whole set of N × K candidates• Set a binary N × K matrix h to specify the “true”
candidate
11 12 1 12
21 22 2 21
1 2 1
... 0 1 ... 0
... 1 0 ... 0( )
... ... ... ... ...... ... ... ...
... 0 0 ... 1
K
K
N N NK NKN KN K N
Q Q Q Q
Q Q Q QQ h Q h
Q Q Q Q
e.g.
![Page 26: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/26.jpg)
How to do? (4/12)
• A new generative hierarchical model
Deformation
Transformation
Image Likelihood
S
1b Lblb ......
nk N KQ Q
z
h
I
Deformation
Transformation
Image Likelihood
( )Q h
![Page 27: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/27.jpg)
How to do? (5/12)
• Deformation– Define prior distribution over the shape S as a
mixture of Gaussian
– Introduce a multinomial distribution z
– Model parameters learned from training samples
, , ,l l l l
0
1
...
0
z
e.g.
![Page 28: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/28.jpg)
How to do? (6/12)
• Similarity Transform
Where– θ={s, R, t} are scale, Rotation, translation
coefficients respectively.– Diagonal observation noise
• measures the noise level of the observation of n-th landmark point.
• • Σ is also learned from training samples and can
updated on fitting phase.– So
n
( ( ), )n Dist T S Y
( )Q h sRS t
![Page 29: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/29.jpg)
How to do? (7/12)
• Image Likelihood– The image likelihood of seeing a landmark
atone particular position Qnk is measured by •
– is generated by feature detector. nk
![Page 30: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/30.jpg)
How to do? (8/12)
• Goal:– Solve b and θ on the basis of the candidate point
set Q.
• MAP problem which can be solved by EM– Posterior with latent variables S, h, z
– Take the expectation of the log over the posterior of the latent variables S, h, z
• Q function:
![Page 31: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/31.jpg)
How to do? (9/12)
• Alignment Algorithm
![Page 32: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/32.jpg)
How to do? (10/12)
• Update Canonical Shape
![Page 33: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/33.jpg)
How to do? (11/12)
• Update Shape Parameters
Shrink by:
![Page 34: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/34.jpg)
How to do? (12/12)
• Identifying Outliers:– Use observation noise model
– Observation noises are unpredictable• Update online
– Change it according to the fitting error between the model prediction and the averaged candidate position
• Define weights to update Canonical Shape– A smaller leads a larger weight to the canonical
shape and less to the observed candidate.
( ( ), )n Dist T S Y
( )Q h sRS t
n
![Page 35: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/35.jpg)
Outline
• Author Introduction.
• Problem Introduction.
• How to do?
• Discussion.
![Page 36: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/36.jpg)
Discussion (1/6)
• Evaluation
![Page 37: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/37.jpg)
Discussion (2/6)
• Handling Extreme Expressions– Number of mixture components is L = 3.
![Page 38: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/38.jpg)
Discussion (3/6)
• Handling Large Occlusion
![Page 39: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/39.jpg)
Discussion (4/6)
• Handling Real World Images
![Page 40: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/40.jpg)
Discussion (5/6)
• Similarity Transform
Where– Diagonal observation noise
• measures the noise level of the observation of n-th landmark point.
• The independence assumption to each landmark is not reasonable.– Markov Network– …
n
( )Q h sRS t
![Page 41: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/41.jpg)
Discussion (6/6)
• The regularization step does not consider the image information anymore
![Page 42: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/42.jpg)
A Robust Shape Model for Multi-view Car Alignment
Yan Li, Leon Gu and Takeo Kanade
![Page 43: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/43.jpg)
Outline
• Problem Introduction.
• How to do?
• Discussion.
![Page 44: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/44.jpg)
Outline
• Problem Introduction.
• How to do?
• Discussion.
![Page 45: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/45.jpg)
Problem Introduction
• Previous shape alignment model– A hypothesis of Gaussian observation noise.– Use all the observed data to fit a regularized
shape.
• This Gaussian assumption is vulnerable to gross feature detection error.
Partial occlusions and spurious background features
![Page 46: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/46.jpg)
Outline
• Problem Introduction.
• How to do?
• Discussion.
![Page 47: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/47.jpg)
How to do? (1/3)
• A hypothesis-and-test approach.– Hypothesis: Bayesian Partial Shape Inference
(BPSI) algorithm•
– Test: The hypotheses are then evaluated to find the one that minimizes the shape prediction error.
1 2{ , ,..., }, { , } { , }N n n nSubsets Q Q Q Q b
![Page 48: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/48.jpg)
How to do? (2/3)
• The observed data– – Random sample from Y
• used to generate hypothesis—shape b and pose θ(s, R, t).
• used to test hypothesis.
• Bayesian Partial Shape Inference (BPSI) algorithm– A MAP problem:– A typical missing data problem can be solved by
EM.
1 2{ , ,..., }, { , }N n n nY Q Q Q Q
pY
hY
![Page 49: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/49.jpg)
How to do? (3/3)
Generate Hypothesis
Test Hypothesis
is the residual between the i-th Corresponding point ofi
and p hY Y
![Page 50: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/50.jpg)
Discussion
![Page 51: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/51.jpg)
Discussion
![Page 52: Paper Reading Dalong Du Nov.27, 2009. Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.](https://reader036.fdocuments.us/reader036/viewer/2022062423/5697bf8e1a28abf838c8cbd3/html5/thumbnails/52.jpg)
Thank you!