Lecture 13 Shape from Shading 2 Looking at finding normal, not distance Normal: Describe the shape...

Lecture 1Lecture 133

Shape from Shading

2

Shape from ShadingShape from Shading

Looking at finding normal, not distanceNormal: Describe the shape

Assuming point light source is far awayp,q are unknowns

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222 1 kkbqkapqpI

Ellipse

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SFS: Data ConstraintSFS: Data Constraint

Given an intensity value I, (p,q) are constrained to be an ellipse

q

p

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222 1 kkbqkapqpI

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Self OccludingSelf Occluding

If know self occluding, we can estimate normal.

Normal for self occluding edges are perpendicular to the edge in 2D

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SFSSFS

In human : tends to assume that light is above

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SFS: SFS: Classical Work

Horn and Schunk Use (p,q)

Problem: Self Occluding p,q undefinedAt occluding edge

dz/dx p ∞, q∞

To rectified this,sphere coordinates (,) are used

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Photometric StereoPhotometric Stereo

2/3 lights

-Given L1, Observe I1-Given L2, Observe I2-Given L3, Observe I3

Have 3 lights at different directions with distance ∞-Turn on L1, take pictures-Turn on L2, take pictures-Turn on L3, take pictures

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I(x,y) = kdId(N.L)= N.L

= Albedo = whiteness

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)( izziyyixxi lllI

z

y

x

zyx

zyx

zyx

III

III

III

I

I

I

333

222

111

3

2

1

4 unknowns : albedo and normal

known known unknown

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I = L.N

3

2

11

I

I

I

L

z

y

x

)(,, 2222222222zyxzyxzyx NNNNNNNNN

2 1

11


4

3

2

291694

294

293

292

N

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Remaining TopicRemaining Topic

•Genetic Algorithm•Neural Network•Motion Processing

•Structure•Tracking (Fovea – Center Of Vision)

•Camera Calibration•Object Recognition Models

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Genetic AlgorithmGenetic Algorithm

Optimization Technique Based on “Survival of Fittest”

1. Population Size – FixedEach solution is an individual

2. Fitness of Individual – Fitness of “Chromosome” (small part) “Goodness”

3. Crossover – Combining Parts of 2 or more individualsNew child is put into population. May die.

4. Mutation – “Random change done to Part of an Individual”

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Charls Darwin – “Survival of Fitness”proposed how species develop

Moth - Industrial Revolution

Yellow Black99% 1%70% 30%20% 80%

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Algorithm:1. Create a random solution of 20 individuals

Sort by fitness { (1,__), (2, __), (3, __), …. }

2. R = Random(0,1)

if (R<0.9) /* Cross Over */

Use 2 or more solutions to create new one

else

Create a new random Individual

Insert new individual in to population if it is fitter than the worst one

Repeat Until the top 20 does not change

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Problem Statement: InputProblem Statement: Input

• The Order Book consists of Many Instances of a Set of Patterns

• Each Piece of garment can be placed at 0 degrees or 180 degrees

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Problem Statement: OutputProblem Statement: Output

W

L• Place all the pieces in the order book to use minimum fabric

length on a fixed width roll• Method: Genetic Algorithm

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About Genetic AlgorithmsAbout Genetic Algorithms

An optimization method that mimics the evolution of life using concepts of survival of the fittest within a fixed population.

Parts of Genetic Algorithm: Individual – a solution with known fitness Population – set of individuals forming the genetic pool Fitness Function – a measure of the goodness of an individual Creating a New Individual through Reproduction:

1. Self Replication 2. Crossover 3. Mutation

Output, result reported as the most fit individual in population.

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Related Work: Related Work: Pargas and Jain 1993 [8] Pargas and Jain 1993 [8]

R. P. Pargas and R. Jain. A Parallel Stochastic Optimization Algorithm for Solving 2D Bin Packing

Problems. IEEE Int. Conf. on A.I. for Applications. 1993.

A stochastic approach to bin packing 2-D figures Similar to genetic algorithms and simulated annealing Has 80% efficiency on regular shapes Tested on objects that can be packed to 100% efficiency For garments, efficiency cannot be 100% We compare to human expert for benchmark

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G. Roussel and S. Maouche, “Improvements About Automatic Lay-Planning For Irregular Shapes on Plain

Fabric” IEEE Proc. Systems Man and Cybernetics, System Engineering, 1993.

Shape layout problem for garment pieces Use a heuristic tree search algorithm called -admissible

algorithm Reasonable results Too much time spent back-tracking Tends to have a local minimum problem

Related Work: Related Work: Roussel and Mouche 1993 Roussel and Mouche 1993 [9][9]

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Related Work: Related Work: Ismail and Hon [11] Ismail and Hon [11]

H.S. Ismail and K.B. Hon. The Nesting of two-dimensional Shapes Using Genetic Algorithms.

Proceedings of The Institution of Mechanical Engineers Part B, Journal of Engineering Manufacture. 1995.

Minimize Raw Mat for cutting 2-D pieces Uses Genetic Algorithms and Heuristics

Simple shapes used Raw Material width not fixed, unrealistic

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Related Work: Related Work: Bounsaythip Bounsaythip et alet al [10] [10]

C. Bounsaythip, S. Maouche and M. Neus. Evolutionary Search Techniques Application in Automated Lay-Planning Optimization Problem. IEEE Int. Conf. on

Intelligent Systems for the 21st Century, 1995.

Minimize unoccupied space by Evolutionary Algorithm Shape representation by Comb Code Efficiency Measure: Length of Raw Mat (Fabric). Used pant garment pieces, regular shapes Good Results due to regular shapes used.

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Related Work: Related Work: Bounsaythip and Maouche [12] Bounsaythip and Maouche [12]

C. Bounsaythip and S. Maouche. Irregular Shape Nesting And Placing With Evolutionary Approach”. IEEE Int.

Conf. On Systems Man and Cybernetics. 1997.

Use the comb code representation for each garment piece Shape placement represented as hierarchical tree Allow orientations of 0, 90, 180, and 270 degrees Crossover: combine parts of tree, removing redundancy Results presented on relatively simple shapes, making it

difficult to assess the efficiency achieved

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Placing Items from Order BookPlacing Items from Order Book

• The Order Book consists of Many Instances of a Set of Patterns

• Each Piece of garment can be placed at 0 degrees or 180 degrees

• Each garment piece is polygonal

• Smooth contours (splines) approximated by convex hull first

1 2 3

4 5 6 7

8 9 10

11 12 13 14

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Placement Method: Check for Placement Method: Check for OverlapsOverlaps

Upon placing a new polygon, must check that:

1. NO vertex is INSIDE other polygons2. NO other polygon’s vertex is INSIDE

Convex Polygons Assumed

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Our Genetic AlgorithmOur Genetic Algorithm

1. Set and Randomly Initialize the Population of size P = 15

2. Divide Individual into chromosome strips. Compute strip efficiency.

3. Crossover, Mutation, and Selection:

Repeat

If random (0, 1) < crossover probability

Create a New Individual by Crossover:

Repeat

Sample for a chromosome from the solution biased by efficiency

Recompute chromosome efficiency based on Order Book balance

Until No Efficient Chromosome Available

Fill Remaining Solution Randomly by Order Book balance

Else

Create New Individual by Mutation: Fill Randomly from Order Book

Insert the solution into the new population

Check for Survival of Fittest P = 15

Until(Population has converged)or(No improvement in Best Solution)

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Step 1: Step 1: Initial Random Population Initial Random Population

S1 = [(5, 1), (3, 0), (4, 1), (1, 1), (2, 0), 15]

S2 = [(1, 0), (3, 0), (2, 1), (3, 0), (4, 0), 17]

S3 = [(5, 1), (3, 0), (7, 1), (1, 1), (2, 0), 20]

S4 = [(1, 0), (5, 0), (4, 0), (3, 1), (2, 0), 21]

S5 = [(1, 0), (3, 0), (5, 0), (2, 1), (4, 0), 23]

S6 = [(4, 0), (5, 0), (1, 1), (2, 0), (3, 0), 25]

S7 = [(3, 1), (4, 0), (5, 1), (2, 0), (1, 0), 27]

S8 = [(5, 1), (4, 0), (3, 1), (2, 1), (1, 0), 29]

S9 = [(3, 0), (2, 0), (1, 0), (5, 1), (4, 1), 32]

S10 = [(4, 1), (3, 0), (1, 1), (2, 1), (5, 1), 34]

An Individual Solution: S = [(F1, O1), (F2, O2),…,(Fn, On), L)]

where S - completed order book Fi - garment piece number

Oi - orientation at 0 or 180 degrees L - Length of Fabric used

5 3

4

1 2

7

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Step 2: Determine StripsStep 2: Determine Strips

W

Lstr1 Lstr2

L

Lstr3 Each Strip is determined bylargest piece along column.

Efficiency of each strip is Computed, used for crossover

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Crossover: Crossover: Sampling Within Population Sampling Within Population

11minmax

max

LLLL

BLB P = LB

LB

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Crossover: Crossover: Sampling for Efficient Sampling for Efficient StripsStrips

11minmax

min

EEEE

BEB P = EB

EB

• After sampling from population for 4 best solutions, Crossover takes place using efficient strips first

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Crossover: Crossover: Efficiency Decreases over Efficiency Decreases over Time Time

• Efficiency decreases as Order Book fills up• Once Efficiency too low, fill remaining items randomly

high lowered

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Mutation:Mutation: New Random Individual New Random Individual

• When Efficiency low, fill randomly is partly like mutation

• Mutation by generating a new random solution

• This new individual usually does not survive

• Our results are compared with layout by human expert

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Experimental Result 1: Experimental Result 1: RectanglesRectangles

6 Sets in Order Book

G.A.: 1:15 Hrs.

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Rectangles by Human ExpertRectangles by Human Expert

Manually: 0:25 Hrs.

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Experimental Result 2: Experimental Result 2: Shirt Pieces Shirt Pieces


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Shirt Pcs. (10 orders) by G.A.Shirt Pcs. (10 orders) by G.A.

G.A.: 51:08 Hrs.

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Shirt Pcs. (10 orders) by HumanShirt Pcs. (10 orders) by Human

Manually: 1:25 Hrs.

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Experimental Result 3: Experimental Result 3: Multi-Edged Shapes by G.A. Multi-Edged Shapes by G.A.


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Multi-Edged G.A. vs. HumanMulti-Edged G.A. vs. HumanG.A.: 0:57 Hrs.

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52

54

56

58

60

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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Iterations

E %1

2

3

5

4

Finding Crossover NumberFinding Crossover Number

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Finding Good Population SizeFinding Good Population Size

50

52

54

56

58

60

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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

E %

Iterations

10

15

20

25 30

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Discussion and ConclusionDiscussion and Conclusion

Main Problem: successive crossover reduces efficiency of good strips.

Efficiency 3-5% lower than human expert, while taking more time. Efficiency depends on the complexity of the piece, making it hard to

compare results among researchers.

high lowered

Lecture 13 Shape from Shading 2 Looking at finding normal, not distance Normal: Describe the shape...

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