Venus Classification Faces Different Faces Same Lighting affects
- Slides: 52
Venus
Classification
Faces – Different
Faces -- Same
Lighting affects appearance
Three-point alignment
Object Alignment Given three model points P 1, P 2, P 3, and three image points p 1, p 2, p 3, there is a unique transformation (rotation, translation, scale) that aligns the model with the image. (SR + d)Pi = pi
Alignment -- comments • The projection is orthographic projection (combined with scaling). • The 3 points are required to be non-collinear. • The transformation is determined up to a reflection of the points about the image plane and translation in depth.
Proof of the 3 -point Alignment: The 3 3 -D points are P 1, P 2, P 3. We can assume that they are initially in the image plane. In the 2 -D image we get q 1, q 2, q 3. The transformation P 1 > q 1, P 2 > q 2, P 3 > q 3, defines a unique linear transformation of the plane, L(x). We can easily recover this transformation. L is a 2*2 matrix. We fix the origin at P 1 = q 1. We have two more points that define 4 linear equations for the elements of L. We now choose two orthogonal vectors E 1 and E 2 in the original plane of P 1, P 2, P 3. We can compute E 1’ = L(E 1), E 2’ = L(E 2). We seek a scaling S, Rotation R, so that the projection of SR(E 1) = E 1’ and SR(E 2) = E 2’. Let SR(E 1) (without the projection) be V 1 and SR(E 2) = V 2. V 1 is E 1’ plus a depth component, that is, V 1 = E 1’ + c 1 z, where z is a unit vector in the z direction. Similarly, V 2 = E 2’ + c 2 z. We wish to recover c 1 and c 2. This will give the transformation between the points (show that it is unique, and it will be possible to recover the transformation). We know that the scalar product (V 1 V 2) = 0. (E 1’ + c 1 z) = 0 Therefore c 1 c 2 = -(E’ 1 E’ 2). The magnitude -(E’ 1 E’ 2) is measurable in the image, call it C 12, therefore c 1 c 2= c 12. Also |V 1| = |V 2|. Therefore (E 1’ + c 1 z) = (E 1’ + c 1 z). 2 2 This implies c 1 - c 2 = k 12, where k 12 is a measurable quantity in the image (it is |E’ 1 | - |E’ 2 |. The two equation of c 1 c 2 are: c 1 c 2 = c 12 2 2 c 1 - c 2 = k 12 2 2 and they have a unique solution. One way of seeing this is by setting a complex number Z = c 1 + ic 2. Then Z = k 12 + ic 12. Therefore, Z is measurable. We take the square root and get Z, therefore c 1, c 2. There are exactly two roots giving the two mirror reflection solutions.
Car Recognition
Car Models
Alignment: Cars
Alignment: Unmatch
Face Alignment
Linear Combination of Views
Linear Combination of Views O is a set of object points. I 1, I 2, I 3, are three images of O from different views. N is a novel view of O. Then O is the linear combination of I 1, I 2, I 3.
Car Recognition
VW – SAAB
LC – Car Images
Linear Combination: Faces
Classification
Structural descriptions
RBC
RBC
Structural Description G 1 Above G 2 Touch G 3 Right-of G 4 G 2 Above Left-of G 4
Fragment-based Representation
Mutual Information Mutual information Entropy Binary variable -H(C) = P(C=1)Log(P(C=1) + P(C=0)Log(P(C=0)
Mutual information H(C) F=1 H(C) when F=1 F=0 H(C) when F=0 I(C; F) = H(C) – H(C/F)
Selecting Fragments
Fragments Selection • For a set of training images: • Generate candidate fragments – Measure p(F/C), p(F/NC) • Compute mutual information • Select optimal fragment • After k fragments: Maximizing the minimal addition in mutual information with respect to each of the first k fragments
Optimal Face Fragments
Face Fragments by Type
Low-resolution Car Fragments Front – Middle - Back
10 5 0 0 1 2 3 Relative object size Relative mutual info. a. 100 x 100 Merit, weight x Merit 15 6 5 4 3 2 1 0 0 1 2 3 4 Relative object size b. 1. 5 1 0. 5 0 - 0. 5 0 1 2 Relative object size 3 100 x Merit, weight 100 x 100 Merit, weight Intermediate Complexity 1. 2 1 0. 8 0. 6 0. 4 0. 2 0 0 0. 5 1 Relative resolution 1. 5 2
Fragment ‘Weight’ Likelihood ratio: Weight of F:
Combining fragments w 1 D 1 wk w 2 Dk
Non-optimal Fragments Fragme nts Optimal size detecti on 11% 95 F/A 0 Small 3% 97 30 Large 33% 39 0 Same total area covered (8*object), on regular grid
Training & Test Images • • • Frontal faces without distinctive features (K: 496, W: 385) Minimize background by cropping Training images for extraction: 32 for each class Training images for evaluation: 100 for each class Test images: 253 for Western and 364 for Korean
Training – Fragment Extraction
Extracted Fragments Korean Fragment Score 0. 92 0. 82 0. 77 0. 76 0. 75 0. 74 0. 72 0. 68 0. 67 0. 65 Weight 3. 42 2. 40 1. 99 2. 23 1. 90 2. 11 6. 58 4. 14 4. 12 6. 47 Western Fragment
Classifying novel images Compare Summed Weights Detect Fragments Decision k. F Westerner w. F Unknown Korean
Effect of Number of Fragments • 7 fragments: 95%, 80 fragments: 100% • Inherent redundancy of the features • Slight violation of independence assumption
Comparison with Humans Algorithm outperformed humans for low resolution images •
Class examples
Distinctive Features
- Thinking language and intelligence
- Argumenterande tal struktur
- Acids and bases song
- Same place same time
- Same place same passion
- Similar figures have the same but not necessarily the same
- Similarity statement
- Same same
- It has 6 rectangular faces 8 vertices and 12 edges
- Whats a homophone
- Heading levels apa 7
- Apa heading
- In text citation multiple authors
- How to in text cite multiple authors apa
- Referent vs sense
- Same sign add different signs subtract
- Things that make us different
- Volume bingo
- Convergent evolution
- Different versions of the same trait
- Thermosoftening plastics examples
- Flame test principle
- Sound will travel at different speeds in different mediums.
- Sound travels fastest through
- What is cultural relativism
- Different angle different story
- Manufactured boards examples
- What affects rate of weathering
- What factor affects the speed of sound wave?
- The new deal affects many groups
- How anxiety affects eyewitness testimony
- A bacterial std that usually affects mucous membranes
- What factor affects the speed of sound wave?
- The perception process
- Chromatic aberration affects reflector telescopes
- How sports affect mental health
- Factors of projectile motion
- Which poetry element affects the poem's sound?
- How culture affects decision making
- What is catalyst and how it affects reaction rate
- How technology affects managerial communication
- Chapter 1 lesson 2 what affects your health
- Hsess
- What affects basicity
- Scale of inquiry affects truth
- Affected ignorance example
- Affects the shape of the graph
- A factor that affects tertiary activity
- Chapter 1 understanding health and wellness lesson 2
- A teacher affects eternity meaning
- Chapter 13 section 3 a global conflict
- How does electrolytes affect the chemical equilibria?
- Culture is affects biology