Download presentation
Presentation is loading. Please wait.
1
Outline Multilinear Analysis
M. A. O. Vasilescu and D. Terzopoulos, “Multilinear Independent Components Analysis,” CVPR 2005
2
Motivations Natural images are generated by the interaction of multiple factors related to scene structure, illumination, and imaging November 10, 2018 Computer Vision
3
Motivations November 10, 2018 Computer Vision
4
Separating Styles from Content
November 10, 2018 Computer Vision
5
Separating Styles from Content
November 10, 2018 Computer Vision
6
Separating Styles from Content
November 10, 2018 Computer Vision
7
Bilinear Model Suppose that we want to represent both style s and content c with vectors of parameters Let ysc denote a K-dimensional observation vector in style s and content class c November 10, 2018 Computer Vision
11
How to Learn the Bases and Coefficients
Learning is done by minimizing total squared error over the entire training set Again the solution is given by a SVD decomposition November 10, 2018 Computer Vision
12
How to Learn the Bases and Coefficients
For symmetric models, we also minimize the total squared error over the training set This is minimized using an iterative procedure November 10, 2018 Computer Vision
13
Classification Example
November 10, 2018 Computer Vision
14
Classification Example
When the model is trained on 10 faces and tested on the remaining one 1-NN achieves an accuracy of 53.9%±4.3% The proposed method achieves 73.9%±6.7% when parameters are determined automatically It achieves 80.6%±7.5% when optimal parameter values are used November 10, 2018 Computer Vision
15
Extrapolation November 10, 2018 Computer Vision
16
Extrapolation November 10, 2018 Computer Vision
17
Translation November 10, 2018 Computer Vision
18
Multilinear Analysis Tensors are multilinear mappings over a set of vector spaces An order N tensor is given by Mode-n vectors are given by They result in a mode-n flattening November 10, 2018 Computer Vision
19
Multilinear Analysis November 10, 2018 Computer Vision
20
Multilinear Analysis November 10, 2018 Computer Vision
21
Multilinear Analysis Mode-n product of a tensor and matrix is given by
A tensor of n factors November 10, 2018 Computer Vision
22
Mode-n SVD November 10, 2018 Computer Vision
23
TensorFaces Weizmann face image database 28 male subjects
photographed in 5 viewpoints, 4 illuminations, and 3 expressions Images are aligned to a reference face using a global rigid optical flow and then downsized by a factor of 3 and cropped, yielding a total of 7943 pixels per image within the elliptical cropping window November 10, 2018 Computer Vision
25
Weizmann Face Dataset November 10, 2018 Computer Vision
26
TensorFaces The dataset is then represented by a tensor of order 5
November 10, 2018 Computer Vision
27
TensorFaces November 10, 2018 Computer Vision
28
TensorFaces November 10, 2018 Computer Vision
32
TensorFaces November 10, 2018 Computer Vision
33
TensorFaces The bases for TensorFaces are given by November 10, 2018
Computer Vision
34
Face Recognition First experiment
TensorFaces are trained on an ensemble comprising images of 23 people, captured from 3 viewpoints (0,±34 degrees), with 4 illumination conditions (center, left, right, left + right) It is tested on other images in this 23 person dataset acquired from 2 different viewpoints (±17 degrees) under the same 4 illumination conditions In this test scenario, the PCA method recognized the person correctly 61% of the time while TensorFaces recognized the person correctly 80% of the time. November 10, 2018 Computer Vision
35
Face Recognition The second experiment
In a second experiment, TensorFaces is trained on images of 23 people 5 viewpoints (0,±17,±34 degrees), 3 illuminations (center light, left light, right light) Tested on the 4th illumination (left + right) PCA yielded a poor recognition rate of 27% while Tensorfaces achieved a recognition rate of 88% November 10, 2018 Computer Vision
36
Dimension Reduction November 10, 2018 Computer Vision
38
N-Mode Orthogonal Iteration Algorithm
November 10, 2018 Computer Vision
41
Multilinear ICA Similar to MPCA, MICA is done using an n-mode ICA algorithm November 10, 2018 Computer Vision
42
Different ICA Architectures
Architecture I ICA computes independent components of DT Architecture II ICA computes independent components of D November 10, 2018 Computer Vision
44
MICA November 10, 2018 Computer Vision
45
MICA November 10, 2018 Computer Vision
46
MICA November 10, 2018 Computer Vision
47
Recognition Experiment
November 10, 2018 Computer Vision
48
TensorTextures Similar idea can be used for image synthesis
November 10, 2018 Computer Vision
49
TensorTextures November 10, 2018 Computer Vision
50
TensorTextures November 10, 2018 Computer Vision
51
TensorTextures November 10, 2018 Computer Vision
52
TensorTextures November 10, 2018 Computer Vision
53
TensorTextures November 10, 2018 Computer Vision
54
TensorTextures November 10, 2018 Computer Vision
55
Comparison November 10, 2018 Computer Vision
Similar presentations
© 2024 SlidePlayer.com. Inc.
All rights reserved.