776 Computer Vision. JanMichael Frahm & Enrique Dunn Spring 2012. Photometric stereo (shape from shading). Luca della Robbia , Cantoria , 1438. Can we reconstruct the shape of an object based on shading cues?. Photometric stereo. S 2. S 1. ???. Assume: A Lambertian object
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Luca dellaRobbia,Cantoria, 1438
S2
S1
???
Sn
Forsyth & Ponce, Sec. 5.4
slide: S. Lazebnik
Forsyth & Ponce, Sec. 5.4
slide: S. Lazebnik
(n × 1)
(n × 3)
(3× 1)
known
known
unknown
slide: S. Lazebnik
This means the normal has the form:
Recovering a surface from normalsIf we write the estimated vector gas
Then we obtain values for the partial derivatives of the surface:
slide: S. Lazebnik
Integrability: for the surface f to exist, the mixed second partial derivatives must be equal:
We can now recover the surface height at any point by integration along some path, e.g.
(for robustness, can take integrals over many different paths and average the results)
(in practice, they should at least be similar)
slide: S. Lazebnik
Forsyth & Ponce, Sec. 5.4
image: R. Szeliski
Phillip Otto Runge (17771810)
slide: S. Lazebnik
Human Luminance Sensitivity Function
slide: S. Lazebnik
Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995
Source: W. Freeman
Source: W. Freeman
p1 p2 p3
The primary color amounts needed for a match:
We say a “negative” amount of p2 was needed to make the match, because we added it to the test color’s side.
p1 p2 p3
p1 p2 p3
Source: W. Freeman
slide: S. Lazebnik
slide: S. Lazebnik
mixing two lights producescolors that lie along a straightline in color space
mixing three lights produces colors that lie within the triangle they define in color space
slide: S. Lazebnik
p1 p2 p3
Find: weights of the primaries needed to match the color signal
Given: a choice of three primaries and a target color signal
?
p1 p2 p3
slide: S. Lazebnik
RGB primaries
RGB matching functions
slide: S. Lazebnik
Matching functions, c(λ)
Signal to be matched, t(λ)
Let c(λ) be one of the matching functions, and let t(λ) be the spectrum of the signal. Then the weight of the corresponding primary needed to match t is
λ
slide: S. Lazebnik
slide: S. Lazebnik
J. S. Sargent, The Daughters of Edward D. Boit, 1882
slide: S. Lazebnik
Source: D. Forsyth
http://www.schorsch.com/kbase/glossary/adaptation.html
slide: S. Lazebnik
correct white balance
incorrect white balance
http://www.cambridgeincolour.com/tutorials/whitebalance.htm
slide: S. Lazebnik
http://www.cambridgeincolour.com/tutorials/whitebalance.htm
slide: S. Lazebnik
slide: S. Lazebnik
slide: S. Lazebnik
J. Van de Weijer, C. Schmid and J. Verbeek, Using HighLevel Visual Information for Color Constancy, ICCV 2007.
slide: S. Lazebnik
Reference: moon
Reference: stone
http://www.cambridgeincolour.com/tutorials/whitebalance.htm
slide: S. Lazebnik
Input
Alpha map
Output
E. Hsu, T. Mertens, S. Paris, S. Avidan, and F. Durand, “Light Mixture Estimation for Spatially Varying White Balance,” SIGGRAPH 2008
slide: S. Lazebnik
Color histograms for image matching
http://labs.ideeinc.com/multicolr
slide: S. Lazebnik
Image segmentation and retrieval
C. Carson, S. Belongie, H. Greenspan, and Ji. Malik, Blobworld: Image segmentation using ExpectationMaximization and its application to image querying, ICVIS 1999.
slide: S. Lazebnik
Skin detection
M. Jones and J. Rehg, Statistical Color Models with Application to Skin Detection, IJCV 2002.
slide: S. Lazebnik
Robot soccer
M. Sridharan and P. Stone, Towards Eliminating Manual Color Calibration at RoboCup.RoboCup2005: Robot Soccer World Cup IX, Springer Verlag, 2006
Source: K. Grauman
Building appearance models for tracking
D. Ramanan, D. Forsyth, and A. Zisserman. Tracking People by Learning their Appearance. PAMI 2007.
slide: S. Lazebnik
slide: S. Lazebnik
1
1
1
1
1
1
1
1
1
“box filter”
Source: D. Lowe
f
Convention: kernel is “flipped”
Source: F. Durand
slide: S. Lazebnik
slide: S. Lazebnik
full
same
valid
g
g
g
g
f
f
f
g
g
g
g
g
g
g
g
slide: S. Lazebnik
Source: S. Marschner
Source: S. Marschner
0
1
0
1
0
1
1
0
2
1
0
1
1
0
1
0
0
1

Original
Source: D. Lowe
Source: D. Lowe
=
detail
smoothed (5x5)
original
Let’s add it back:
+
=
original
detail
sharpened
–
slide: S. Lazebnik