image processing 1 - aura astronomy · mauricio cerda icbm, cimt, faculty of medicine universidad...
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Mauricio CerdaICBM, CIMT, Faculty of Medicine
Universidad de [email protected]
www.scian.cl
Image Processing 1images, segmentation, shape
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Outline
Castañeda V, Cerda M, 2014Computational methods for analysis of dynamic events in cell migration
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Outline
1. Introduction
• Images• Segmentation
2. Descriptors
• Shape
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• A digital image can be defined as a function over a discrete space
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Digital Images
– A typical 2D image model isthe raster image: array(matrix) of pixeles in cartesian coordinates (x, y)
– A numeric value forbrightness (intensity) orcolor is associated to eachpixel
Aubert & Kornprobst (2006)Mathematical Problems In Image Processing
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• Greyscale image
– A brightness (intensity) level is defined for each pixel
Digital Images
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I(290,267) = 220
8 bit greyscale image
A n bit greyscale imageencodes up to 2nintensity values
Binaryvalue
Decimal value
0000 0000 0 (black)
0000 0001 1
0000 0010 2
0000 0011 3
0000 0100 4
0000 0101 5
0000 0110 6
0000 0111 7
0000 1000 8
… …
1111 1011 251
1111 1100 252
1111 1101 253
1111 1110 254
1111 1111 255 (blanco)
Digital Images
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• RGB image
– Three channels for respective primary colors:Red, Green, Blue
• Other color spaces are HSV, LAB
Digital Images
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• It is possible to define color tables (or lookup tables, LUTs) for visualization purposes. A grayscale image can bedisplayed using a green scale.
r g b 000::::0::0
012::::200::255
000::::0::0
Digital Images
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• Segmentation
– The partitioning of a given image into regions of interest (ROIs) according to given criteria (e.g. color).
– After segmentation, further characterizations can be performed upon the resulting ROIs.
Shapiro LG and Stockman GC (2001):“Computer Vision”, pp 279-325New Jersey, Prentice-Hall
Image Analysis
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Sky / FlatSol 3, Mars Pathfinder Mission
Dust / Horizon Final segmentation
…etc…
Segmentation
Images from NASA
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Segmentation
Max Z-Project from confocal microscopy of Fundulus N. [data by German Reig 2015]
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Segmentation
Problems
• Lack of absolute criteria or standards(Ground Truth, Gold Standard [1,2])
• Missing or erroneus information(e.g. non-specific markers in samples)
• What to do? A “good” (i.e. carefully performedand controlled) acquisition ease this process
[1] Jason D. Hipp et all. Tryggo: Old norse for truth: The real truth about ground truth. New insights into the challenges of generating ground truth maps for WSI CAD algorithm evaluation. Pathol. Inform 2012, 3:8
[2] Luc Bidaut, Pierre Jannin. Biomedical multimodality imaging for clinical and research applications: principles, techniques and validation. In Molecular Imaging:Computer Reconstruction and Practice (NATO Science for Peace and Security Series B: Physics and Biophysics), Springer, 2008, ISBN-13: 978-1402087516.
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• Segmentation is the first step toward further quantifications
Parameter estimation…
Endoplasmic reticulum in a COS-7 cellO Ramírez, L Alcayaga (2012)
•Size: area, perimeter•Boundary: inflections, shape•Topology: connectivity, endpoints
Lipid monolayersJ Jara (2006), Fanani et al (2010)
Segmentation
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Segmentation
1. Classic approaches (filters)– Thresholding– Matrix convolution filters + threshold– Mathematical morphology
2. Advanced approaches– Shape priors (pattern matching)– Deformable models (active contours)
• parametric• implicit
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• Threshold filtersegmentation: ROIs (white) / background (black)
Intensity histograms
Segmentation – basics
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• Convolution– Lots of filters based on this principle
http://en.wikipedia.org/wiki/Convolution
• Matrix convolution, in our case, is an operation between two matrices, namely…– the input image, I– a kernel, K
Adapted from James Matthews, 2002http://www.generation5.org/content/2002/convolution.asp
Segmentation – basics
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• Intensity gradients (discrete approximation)
»¶¶xI
»¶¶yI
Segmentation – basics
flat + -
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18
I = I(x, y)
x
y
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19
IxIy
x
y
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20
“Edgemap”|▼I|=|Ix|+|Iy|
x
y
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• Intensity gradients (discrete approximation)
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Segmentation – basics
flat + -
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ïþ
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Laplace
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• Kernels…
pixel1=D=D yx
Segmentation – basics
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• Morphology based filters– Example: size selection
Input greyscale image After thresholding…
Size selectionHow to define a size-select algorithm?
Segmentation – basics
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• Mathematical morphology
Segmentation – basics
Dilate
Erode
What is B?
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• Mathematical morphology
Segmentation – basics
To open:
To close:
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• “Some” times more information is needed in order to achieve a good segmentation (see additional material)
Segmentation – basics
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Outline
27
1. Introduction
• Images• Segmentation
2. Descriptors
• Shape
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Shape descriptors
Motivation
2D image and segmentations, Lisette Leyton’s Lab (BNI) Original image and 3D segmentation , Karina Palma (LEO, BNI).
Ex. 1Shape and structure analysis of fibroblast actin fibers (astrocytes)
Ex. 2Zebrafish parapineal organ neuron
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1. Geometrical descriptors: location, perimeter, area, volume, curvature
2. Moments of morphology (order 0-2)3. Topology in computer science (skeletons)
Shape & topology descriptors…
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Location, perimeter, area and volume partially describe an object, but not its shape.
Moments of morphology
Original image (2D),Prof. Lisette Leyton
30
How to quantify the amount of roundness of an object?
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Variance
Moments of morphology
31
Axes U and V maximize the variance in U
Covariance
Positive covariance Zero covariance
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We look for two parameters to characterize the binary ROI…
Moments of morphology
32
X
Y
α
L1Semi-major axis
L2
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• If the variance/covariance matrix is diagonal for a certain rotation α,
• Semi-major axis length l is a function of second-ordermoments
Moments of morphology
33
L21 =
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Second order moments of morphology describe a ROI main axis (principal components)
Moments of morphology
• The major axis corresponds to thedirection with the biggest variance.
• The secondary axis (minor in 2D) isorthogonal to the major axis, giving in 3D the direction of the second biggestvariance.
• The third axis (3D) is orthogonal to themajor and secondary axes.
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Moments of morphology
Principal axes are useful objectdescriptors because…
• they directly define the objectlength, height, and width
• using principal axes, similaritiesbetween objects can be found
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Parámetros del Programa
By combining the principal axes, we can define Elongation, Relative Elongation, and Flatness.
evevElong°°
-=121
2°ev
1°ev 3°ev
1°ev >> 2°evElong. ~ 1
2°ev
1°ev 3°ev
evevElongR°°
-=131.
1°ev >> 3°evR. Elong. ~ 1
evevFlatness°°
-=231
2°ev
1°ev 3°ev
2°ev >> 3°evFlatn. ~ 1
Moments of morphology
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Resumen
• The variance allows to computer principal axes (eigenvectors) and to quantify dispersion for each principal axis direction (eigenvalues)
• Composed parameters between eigenvalues deliver morphological parameters like elongation or flatness
• Higher order moments describe more detailed information like asymmetry or kurtosis
Moments of morphology - remarks
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• EXERCISE: Compute elongation [python notebook]