Shape From Texture

Nick Vallidis

March 20, 2000

COMP 290 Computer Vision

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Why Shape from Texture?

• Texture provides our visual systems with a huge amount of information

• Computers should gain lots of information from it too then, right?

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Sometimes texture is all you need

Source: Computer Analysis of Visual Texturesby Fumiaki Tomita and Saburo Tsuji

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So what is texture?

• One very restrictive definition: “Repeating patterns of local variations in image intensity which are too fine to be distinguished as separate objects”

• The patterns that repeat are sometimes referred to as texels– NOTE: not the same as a graphics texel as it is

made of more than one pixel!

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Tell me more about textures!

• There are basically two kinds:– Deterministic– Statistical

• It’s pretty much man-made (deterministic) vs. natural (statistical)

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Deterministic Texture Examples

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Statistical Texture Examples

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What’s the general approach?

• Texture segmentation– hard! This is still a big research area.

• Texture classification– There are many methods to do this.

• Shape from texture– We’ll just pretend we can do the first two...

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Many things to many people

• There isn’t “one” shape from texture algorithm.

• Textures are complex so there are many different aspects that can be taken advantage of.

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Comparison of a few approachesAuthor(year)

Surface cue Surfacetype

Originaltexture

Projectiontype

Bajcsy(1976)

Texture-gradient

Planar Unknown perspective

Ohta(1981)

Texture-gradient

Planar Unknown perspective

Nakatani(1980)

Converging-lines

Planar Parallel-lines

perspective

Kender(1979)

NTPM* Planar Known Ortho-graphic

Walker(1984)

Shape-distortion

Curved Unknown Ortho-graphic

*Normalized Texture Property Map

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Surface Orientation from Texture

• Statistical texture method

• Assumptions:– Texels are small line segments: “needles”– Needles distributed uniformly (in both angle

and position)– Only one, approximately-planar surface– Orthographic projection

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What we’re calculating

• The tilt, , and slant, , of the plane:

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Where do we get needles?

• Imagine straw covering a plane

• Use an edge detector and we’ve got needles! (this even gives us orientation!)

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Ok, so what do we do with them?

• The metric we’re working from is the needle’s angle with the X axis:

X axis

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Define some random quantities

• For every needle, define a vector: [cos(2), sin(2)]

• So we can tell the angle of the plane by the distribution of these vectors on the unit circle!

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Calculate some statistics

• Find the center of mass of the vectors:

N

iiN

C1

2cos1

N

iiN

S1

2sin1

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Calculate some statistics

• But C and S can be put in terms of and : (only holds for orthographic

projection)

cos1

cos12cos

C

cos1

cos12sin

S

(Sorry, no proof on this one…)

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We can solve for the orientation!

• By converting C and S to polar coordinates, we get a simple form to solve for and :

Q

Q

1

1arccos

)2(mod2

(where and )22 SCQ C

Sarctan

2

1

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Example!Original Texture/Needles

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Original vector distribution

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Rotated needles

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Rotated vector distribution

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Other texels

Source: ComputerAnalysis of VisualTextures

Source: Scale-Space Theory inComputer Vision by TonyLindeberg

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Other Texels II