Touching chromosomes, overlapping chromosomes, single chromosomes and their convexity defects

Let's start with convexity defects (blue circles) detected in totally overlapping chromosomes:

The convexity defects can be directly used to resolve the two overlapping chromosomes, the script is used with d>1000 (see the two previous posts).

When the chromosomes partially overlap, we can have less than four points detected:

As in the previous post, touching chromosomes produce convexity defects. In the following example of two small chromosomes, the two convexity defects detected surrounds the "touching region" . Tracing a segment between the two points would cut the particle (green contour) into two complete chromosomes.

 However touching chromosomes do not always produce  "good" pair of convexity defects which could be used to separate them. In the two following examples, we have two kinds of convexity defects (CD): CDs closed to the touching domain (at coordinates:grossly [30;20] or [40;75] )and CDs near the  centromere (coordinates [35;60]).

Two CDs near the centromere, one CD near the touching region.

Two CDs around the touching region, one CD near the centromere

 In the following cluster of four human chromosomes, only CDs corresponding to the three touching domains were detected. Note that a point at (50,80) corresponding to a touching domain in a highly bended part of the contour and quit far from the convex hull (red) was not detected:

Convexity defects are also detected on single chromosomes keeping the same parameters (d>1000). Let's start with two good cases where the pair of CDs are around the centromere:

The chromosome morphology can alter the detection:

In all the previous example, only CDs with d>1000 were kept. Lowering the  threshold for the d value increases the number of CDs, here is some examples with single chromosomes:

Probably HSA2 chromosome: d>100 : Two CDs are close to the centromere, the others are false positive CD

d>500 : one false positive CD for centromere detection

d>1000 : only one CD near the centromere is detected

For a smaller chromosome (may be chromosome 17), we get:

CD with d>1000

CD with d>500

Playing around with opencv convexity defects

Modifying a little the code of the previous post, removes the points too close to the convex hull:

Edit the end of the script as follow:

    cv2.line(img,start,end,[255,0,0],1)
    if d>1000:
        cv2.circle(img,far,3,[0,0,255],2)

Convexity defects in a cluster of mouse chromosomes

Just a little trial to explore cv2.convexityDefects() on a cluster of mouse chromosomes:

The cluster consists in five touching mouse chromosomes. The aim is to use cv2 to display the contour of the particle, its convex hull, and to see what it is possible to do with convexityDefects function implemented in OpenCv 2.4.2 which provides now the big advantage of handling numpy array. The python script used is largely inspired from abid rahman's blog:

# -*- coding: utf-8 -*-
"""
Created on Wed Jul  4 14:43:42 2012

@author: jean-pat
"""

import cv2
import numpy as np
import os
import pylab as plb
print cv2.__version__

user=os.path.expanduser("~")
workdir=os.path.join(user,"QFISH","JPPAnimal","JPP52","11","DAPI","particles")

file="part25.png"
complete_path=os.path.join(workdir,file)

img = cv2.imread(complete_path)
gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
ret,gray = cv2.threshold(gray,1,255,0)
print ret
gray2 = gray.copy()
mask = np.zeros(gray.shape,np.uint8)

contours, hier = cv2.findContours(gray,cv2.RETR_LIST,cv2.CHAIN_APPROX_SIMPLE)
print hier
cv2.drawContours(img,contours,0,(0,255,0),1)
cnt = contours[0]
hull = cv2.convexHull(cnt,returnPoints = False)
#print hull
approx = cv2.approxPolyDP(cnt,0.05*cv2.arcLength(cnt,True),True)
print 'approx',approx

print 'contours',type(cnt), cnt.dtype, len(contours)
defects = cv2.convexityDefects(cnt,hull)
print defects
for i in range(defects.shape[0]):
    s,e,f,d = defects[i,0]
    start = tuple(cnt[s][0])
    end = tuple(cnt[e][0])
    far = tuple(cnt[f][0])
    cv2.line(img,start,end,[255,0,0],1)
    cv2.circle(img,far,5,[0,0,255],1)

plb.imshow(img)
plb.show()

    

The result is :

Strangely, some convexity defects (blue circles) of the particle contour (green curve) are very close to the particle convex hull (red curve). Four defects are detected on the contour where the chromosomes touch each other as waited. Those contact regions correspond to "neck" on the contour curve, and only one side of the neck is detected.
At first sight, there is nine false positive points, four well detected points and four non detected points (the other side of the "necks").

From the script, the content of the defect variable is:

[[[  214   216   215   689]]
[[  216   218   217   114]]
[[    0    30    19  2444]]
 [[   30    32    31   234]]
 [[   32    34    33   201]]
 [[   34    38    37   278]]
 [[   38    71    56  5658]]
 [[   72    78    73   114]]
 [[   78    94    87  3133]]
 [[   96    98    97   114]]
 [[   98   106   101   297]]
 [[  106   120   111   364]]
 [[  121   212   179 12452]]]

The convexity defect is a list of vectors of the form:

(start_index, end_index, farthest_pt_index, fixpt_depth)

so it should be possible to filter the points too close to the convex hull.

Building OpenCv 2.4.2 on Ubuntu 12.04

In Ubuntu 12.04 only OpenCv 2.3 is available. To exploit the examples in Abid Rahman's blog, at least OpenCv 2.4 is necessary.

To install OpenCV 2.4.2, open you package manager (synaptics) and uninstall if necessary previous OpenCv version. Check if the required/optionnal libraries are installed, for example:

                          

                          Commit Log for Wed Jul  4 21:38:54 2012

                          Les paquets suivants ont été installés :
                          libtbb-dev (4.0+r233-1)
                          libtbb-doc (4.0+r233-1)
                          libtbb2 (4.0+r233-1)
                          tbb-examples (4.0+r233-1)

cmake must be installed, it's convenient to install cmake-gui too. Download OpenCv 2.4.x (here 2.4.2) and uncompress the archive in some directory. Make an other directory to build OpenCV:

For example, in a directory called Applications,  the OpenCv source code is in OpenCv-2.4.2 and an empty directory Build OpenCv242.
Run cmake-gui, it can be found from the dash:

looking for CMake with the Dash

Once cmake run, select the directory containing OpenCv source code, and the target directory that will contain the build OpenCv:

CMake gui running after having selected the source code directory and the build directory

Within cmake, check the different options that are needed (tiff support, python ...), click on the configure button, then on generate. If everything went fine, open the destination directory, open a console in it and type the commands:

                                                        make

then 

                                                         sudo make install

The options selected can be found in the CMakeCache.txt file.

The installation can be checked by opening a ipython shell and importing cv2 as follow:

ipython shell after cv2 importation

The auto completion can find some function implemented in OpenCv (cv2).