MAURICIO CERDA LAB BIO-RELATED : IMAGE PROCESSING METHODS FOR MICROSCOPY IMAGING
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1 MAURICIO CERDA LAB BIO-RELATED : IMAGE PROCESSING METHODS FOR MICROSCOPY IMAGING - La Serena, 8/24/2017 -
2 OUTLINE Image processing? Segmentation (clustering) Shape description (PCA) Lab: challenge!
3 IMAGE PROCESSING: IMAGE Image: is an artifact that depicts visual perception, for example, a photo or a two-dimensional picture, that has a similar appearance to some subject usually a physical object or a person, thus providing a depiction of it [wikipedia, 2017].
4 IMAGE PROCESSING Raster image: Array or matrix of pixels with spatial coordinates I(x,y). A numerical value or color per location.
5 IMAGE PROCESSING Vectorial image: Defined by basic functions (points, lines), instead of pixels. To be displayed on screen needs to be rasterized (transforms to a raster image). Raster or Vectorial in a paper?
6 IMAGE PROCESSING We want to process images to understand biological systems (models): Tissue development Medical imaging (parasites counting)
7 IMAGE PROCESSING: TISSUE DEVELOPMENT killifish (uruguay) eggs confocal microscope (U-Chile) z y z x Austrolebias nigripinnis HPF, membrane marked with actine EGFP. How cells migrate over other cells?
8 IMAGE PROCESSING: CHAGAS
9 IMAGE PROCESSING: PARASITES Pregnancy?
10 IMAGE PROCESSING: PIPELINE
11 IMAGE SEGMENTATION The simplest segmentation a manual global threshold [demo FIJI]. segmentation (>46) raw image segmentation (>158)
12 IMAGE SEGMENTATION But, it looks like?
13 IMAGE SEGMENTATION We will start with two objects: cells, and background. We don t have examples (!) This is another kind of learning problem: Supervised: regression, classification Unsupervised: clustering
14 IMAGE SEGMENTATION We can model it as how to discover the best k groups or clusters at a pixel level. K-means clustering (k=3): Random centroids clusters assignation + voronoi diagram centroids re-computation cluster assignation + voronoi diagram K-Mean pseudocode [demo FIJI]:
15 IMAGE SEGMENTATION But we can also make examples! (label data) In that case, segmentation may be a supervised problem. Let s try to solve it as a Random Forest problem [demo FIJI]. How can we decide?
16 SHAPE DESCRIPTION: MOTIVATION If images are segmented, we can easily count objects. But, we cannot tell the difference between small and big or circle-like vs elongated cells.
17 SHAPE DESCRIPTION: IMAGE AS DISTRIBUTION The image as a set of pixels We can always find a direction to maximize variance
18 SHAPE DESCRIPTION: IMAGE AS DISTRIBUTION We can always find a direction to maximize variance Equivalent to diagonalize covariance matrix
19 SHAPE DESCRIPTION: GEOMETRICAL VIEW We look for a rotation where covariance matrix is diagonal.
20 SHAPE DESCRIPTION: GEOMETRICAL VIEW If we call the rotation Covariance matrix is diagonal (eigenvectors): If we assume a size 1 vector covariance matrix
21 SHAPE DESCRIPTION: GEOMETRICAL VIEW
22 SHAPE DESCRIPTION: GEOMETRICAL VIEW With 1st eigenvalue we can measure the length (l) of the object in its intrinsic shape.
23 SHAPE DESCRIPTION: ECCENTRICITY We can now define eccentricity as: Elong = l 1-2 l 1 R. Elong = 1- l3 l 1 Flatness = l 1-3 l 2 λ 1 >> λ 2 Elong. ~ 1 λ 1 >> λ 3 R. Elong. ~ 1 λ 2 >> λ 3 Flatn. ~ 1
24 SHAPE DESCRIPTION: FAST COMPUTATION We can compute it fast in binary images with image moments. Order 0 Order 1
25 SHAPE DESCRIPTION: FAST COMPUTATION With 2nd order moments covariance matriz is:
26 SHAPE DESCRIPTION: PCA To find the rotation is known as Principal Component Analysis (PCA). Multiple applications, eg. select eigenvectors to simplify distribution (objects) to a few numbers. PCA in FIJI [demo].
27 LAB: CHALLENGE Challenge 1: to estimate the number of parasites, BeWo cells, and their eccentricity.
28 LAB: CHALLENGE Count the number of infected cells by assigning (eg Voronoi) parasites to BeWo cells. Acta Trop Mar;143: doi: /j.actatropica Epub 2014 Dec 29.
29 THANKS F-Medicine F-Engineering SCIAN-Lab Steffen Härtel Mauricio Cerda Victor Castañeda Jorge Jara Marilyn Gatica Paula Llanos Alejandro Lavados Juan Jose Alegría Jimena López Jorge Mansilla Lucas Ale Jorge Toledo LEO-Lab Miguel Concha German Reig Loreto López Eduardo Pulgar Lab Chagas Ulrike Kämmerling Anita Liempi Hospital Clínico U-Chile Computer Science Nancy Hitschfeld Physics Rodrigo Soto Nestor Sepúlveda Anillo: MAURICIO CERDA
30 SHAPE DESCRIPTION: HIGH DIMENSION?
31 SHAPE DESCRIPTION: HIGH DIMENSION? How to understand an image in high dimension? n nmx1 m
32 SHAPE DESCRIPTION: HIGH DIMENSION? For 2D images, we now have a nm size vector per image n n m m nmx1 nmx1
33 SHAPE DESCRIPTION: HIGH DIMENSION? Now, each image is a point in your feature space.
34 SHAPE DESCRIPTION: COVARIANCE MATRIX Now, each image is a point in our feature space. (column vector) (mean of row 1)
35 SHAPE DESCRIPTION: COVARIANCE MATRIX If (centered data) We can diagonalize the matriz (eg. using SVD) Eigenvectors Eigenvalues (diagonal matrix)
36 SHAPE DESCRIPTION: PCA If eigenvalues are sorted from higher to lower. The first eigenvector will indicate the direction that maximizes variance. If the input vector are size nm, how many eigenvector are in the base?
37 SHAPE DESCRIPTION: PCA AS DESCRIPTOR Example. Face representation (eigenfaces) from a set of k photos form the same person. 1 2 k
38 SHAPE DESCRIPTION: PCA AS DESCRIPTOR Example. Face representation (eigenfaces). The first 10 eigenvectors are:
39 SHAPE DESCRIPTION: PCA AS DESCRIPTOR Example. Face representation (eigenfaces). We can use it as a way to reduce dimensionality:
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