a discriminatively trained, multiscale, deformable …efros/courses/lbmv09/presentations/...a...
TRANSCRIPT
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A Discriminatively Trained, Multiscale, Deformable Part Model
Edward Hsiao
16-721 Learning Based Methods in Vision
February 16, 2009
P. Felzenszwalb, D. McAllester, and D. Ramanan
Images taken from P. Felzenszwalb, D. Ramanan, N. Dalal and B. Triggs
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Overview
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Histogram of Oriented Gradients (HOG)
• Split detection window into 8x8 non-overlapping pixel regions called cells
• Compute 1D histogram of gradients in each cell and discretize into 9 orientation bins
• Normalize histogram of each cell with the total energy in the four 2x2 blocks that contain that cell -> 9x4 feature vector
• Apply a linear SVM classifier
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Histogram of Oriented Gradients (HOG)
9 orientation bins0 - 180° degrees
block
cell
9x4 feature vector per cell
normalizeFeature vector
f = […,…,…, ,…]
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Histogram of Oriented Gradients (HOG)
9 orientation bins0 - 180° degrees
block
cell
9x4 feature vector per cell
normalizeFeature vector
f = […,…,…, ,…]
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Histogram of Oriented Gradients (HOG)
9 orientation bins0 - 180° degrees
block
cell
9x4 feature vector per cell
normalizeFeature vector
f = […,…,…, ,…]
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Histogram of Oriented Gradients (HOG)
9 orientation bins0 - 180° degrees
block
cell
9x4 feature vector per cell
normalizeFeature vector
f = […,…,…, ,…]
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SVM Review
1=⋅ xw
1−=⋅ xw
1=c
1−=c
1)( ≥⋅ ii xwc
1)( subject to 21 minimize 2 ≥⋅ ii xwcw
w2
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Hinge Loss))(1 ,0max( ii xwc ⋅−
0)(1 >⋅− ii xwc if incorrectly classified or inside margin
1
1correctly classified
marginalincorrectly classified
))(1 ,0max(minarg1
2 ∑=
⋅−+n
iii
wxwcwλ
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HOG & Linear SVM
not pedestrian
pedestrian
0<⋅ fw
0>⋅ fw
HOG space
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Histogram of Oriented Gradients (HOG)
Test image HOG descriptor
Positive components
Negative components
w+
w-
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Average Gradients
person car motorbike
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Deformable Part Models
Root filter8x8 resolution
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Deformable Part Models
Root filter8x8 resolution
Part filter4x4 resolution
Quadratic spatial model
2,
2,,, iiyiixiiyiix ybxbyaxa +++
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HOG Pyramid
),( pHφ concatenation of HOG features in a subwindow of the HOG pyramid H at position p = (x,y,l)
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Deformable Part Models
Root filter F0 Part filters P1 …Pn
),,,,( iiiiii basvFP =
score =
filter response part placement
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Part Models
),,,,( iiiiii basvFP =
root filter
part filter
iv1,is
2,is
iF
2,
2,,, iiyiixiiyiix ybxbyaxa +++
Quadratic spatial model
iyix bb ,, <
iyix bb ,, =
0≥ib
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Star Graph / 1-fan
root filterposition
part filterpositions
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Distance Transforms
quadratic distance specified by ai and bi
filter response
part anchor location part position
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Quadratic 1-D Distance Transform
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Quadratic 1-D Distance Transform
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Quadratic 1-D Distance Transform
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Distance Transforms in 2-D
input column distance transform
fulldistance transform
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Latent SVM
HOG & Linear SVM
)()( xwxfw Φ⋅=
0Fw =
)~,~,~,~, . . . ,~,~,~,~
),),((, . . . ),),((),),(((),(222
12
111
10
nnnn
n
yxyxyxyxpxHpxHpxHzx φφφ=Φ
))(1 ,0max(minarg1
2*i
n
iwi
wxfyww ∑
=
−+= λ
),(max)()(
zxwxfxZzw Φ⋅=
∈
),,...,,,,...,( 110 nnn babaFFw =
)),(()( 0pxHx φ=Φ
Deformable Parts & Latent SVM
))(1 ,0max(minarg1
2*i
n
iwi
wxfyww ∑
=
−+= λ
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Semi-convexity
convex in w
∑∑∈∈
++−+=negi
iwposi
iww
xfxfww ))(1 ,0max())(1 ,0max(minarg 2* λ
•If fw(x) is linear in w, this is a standard SVM (convex)
•If fw(x) is arbitrary, this is in general not convex
•If fw(x) is convex in w, the hinge loss is convex for negative examples (semi-convex)- hinge loss is convex in w if positive examples are restricted to single choice of Z(x)
convex
),(max)()(
zxwxfxZzw Φ⋅=
∈
∑∑∈∈
++Φ⋅−+=negi
iwposi
iiw
xfzxwww ))(1 ,0max()),(1 ,0max(minargˆ 2λ
Optimization is now convex!
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Coordinate Descent
1. Hold w fixed, and optimize the latent values for the positive examples
2. Hold {zi} fixed for positive examples, optimize w by solving the convex problem
),(maxarg)(
zxwzixZz
i Φ⋅=∈
∑∑∈∈
++Φ⋅−+=negi
iwposi
iiw
xfzxwww ))(1 ,0max()),(1 ,0max(minargˆ 2λ
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Data Mining Hard Negatives
positive examplesnegative examples
HOG Space
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Data Mining Hard Negatives
positive examplesnegative examples
HOG Space
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Data Mining Hard Negatives
positive examplesnegative examples
HOG Space
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Data Mining Hard Negatives
positive examplesnegative examples
HOG Space
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Data Mining Hard Negatives
positive examplesnegative examples
HOG Space
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Data Mining Hard Negatives
positive examplesnegative examples
HOG Space
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Data Mining Hard Negatives
positive examplesnegative examples
HOG Space
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Model Learning Algorithm
• Initialize root filter
• Update root filter
• Initialize parts
• Update model
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Root Filter Initialization
• Select aspect ratio and size by using a heuristic- model aspect is the mode of data- model size is largest size > 80% of the data
• Train initial root filter F0 using an SVM with no latent variables- positive examples anisotropically scaled to aspect and size of filter- random negative examples
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Root Filter Update
• Find best scoring placement of root filter that significantly overlaps the bounding box
• Retrain F0 with new positive set
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Part Initialization
• Greedily select regions in root filter with most energy
• Part filter initialized to subwindow at twice the resolution
• Quadratic deformation cost initialized to weak Gaussian
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Model Update
• Positive examples – highest scoring placement with > 50% overlap with bounding box
• Negative examples – high scoring detections with no target object (add as many as can fit in memory)
• Train a new model using SVM
• Keep only hard examples and add more negative examples
• Iterate 10 times
positive example
hard negative example
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Results – PASCAL07 - Person
0.9562 0.87200.9519 0.8298
0.7723 0.7536 0.7186 0.6865
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Results – PASCAL07 - Bicycle
1.4806 1.4282 1.3662 1.3189
2.1838 1.81492.1014 1.6054
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Results – PASCAL07 - Car
1.1035 1.0645 1.0623 1.0525
1.5663 1.25941.3875 1.1390
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Results – PASCAL07 - Horse
-0.4573 -0.5014 -0.5106 -0.5499
-0.3007 -0.4138-0.3946 -0.4254
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Results - Person
-1.1999 -0.7230 -0.0189 0.1432 0.3267
So do more realistic images give higher scores?
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Superhuman
2.56!
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Gradient Domain Editing
gx gx'
gy gy'
Decompose Edit Reconstruct
∂∂
∂∂
=∇yx
,
f(x,y)
gf =∇
gf ∇=∇2
(Solve Poisson Equation)
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Generating a “person”
9 orientation bins 18 orientation binsfor positive and negative
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Generating a “person”
gx
gy
initial “person”initial orientation bin assignments
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Simulated Annealing
highercost
−−=
TccP currentnew )(exp
T is initially high and decreases with number of iterations
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Person
Score: 2.56 Score: 0.96
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Generated Images
Score: 3.14
Car
Score: 0.84
Horse
Score: 1.57
Score: -0.30
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Generated Images
Score: 2.63
Bicycle
Score: 0.80
Cat
Score: 2.18
Score: -0.71
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Gradient Erasing
OriginalScore: 0.83
ErasedScore: 2.78
Difference image
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Gradient Erasing
OriginalScore: -0.76
ErasedScore: 0.26
Difference image
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Gradient Addition
Score: 0.83 Score: 3.03
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Gradient Addition
Score: 2.15
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Discriminatively Trained Mixtures of Deformable Part Models
P. Felzenszwalb, D. McAllester, and D. Ramanan
http://www.cs.uchicago.edu/~pff/latentSlide taken from P. Felzenszwalb
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Questions?
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Thank You