## Thursday, March 14, 2013

### Histograms - 4 : Backprojection

Hi friends,

Today, we will look into histogram back-projection. It was proposed by Michael J. Swain , Dana H. Ballard in their paper "Indexing via color histograms".

Well, what is it actually in simple words? It is used for image segmentation or finding objects of interest in an image. In simple words, it creates an image of the same size (but single channel) as that of our input image, where each pixel corresponds to the probability of that pixel belonging to our object. So in short, the output image will have our object of interest in white and remaining part in black. Well, that is an intuitive explanation.

(In this article, I would like to use a beautiful image of a bunch of rose flowers. And the image credit goes to "mi9.com". You can get the image from this link : http://imgs.mi9.com/uploads/flower/4649/rose-flower-wallpaper-free_1920x1080_83181.jpg)

How do we do it ? We create a histogram of an image containing our object of interest (in our case, the rose flower, leaving leaves and background). The object should fill the image as far as possible for better results. And a color histogram is preferred over grayscale histogram, because color of the object is more better way to define the object than its grayscale intensity. ( A red rose flower and its green leaves may have same intensity in grayscale images, but easily distinguishable in color image). We then "back-project" this histogram over our test image where we need to find the object, ie in other words, we calculate the probability of every pixel belonging to rose flower and show it. The resulting output on proper thresholding gives us the rose flower alone.

So let's see how it is done.

Algorithm :

1 - First we need to calculate the color histogram of both the object we need to find (let it be 'M') and the image where we are going to search (let it be 'I').

import cv2
import numpy as np
from matplotlib import pyplot as plt

#roi is the object or region of object we need to find
hsv = cv2.cvtColor(roi,cv2.COLOR_BGR2HSV)

#target is the image we search in
hsvt = cv2.cvtColor(target,cv2.COLOR_BGR2HSV)

# Find the histograms. I used calcHist. It can be done with np.histogram2d also
M = cv2.calcHist([hsv],[0, 1], None, [180, 256], [0, 180, 0, 256] )
I = cv2.calcHist([hsvt],[0, 1], None, [180, 256], [0, 180, 0, 256] )


2 - Find the ratio R = M/I

R = M/(I+1)


3 - Now backproject R, ie use R as palette and create a new image with every pixel as its corresponding probability of being target. ie B(x,y) = R[h(x,y),s(x,y)] where h is hue and s is saturation of the pixel at (x,y). After that apply the condition B(x,y) = min[B(x,y), 1].

h,s,v = cv2.split(hsvt)
B = R[h.ravel(),s.ravel()]
B = np.minimum(B,1)
B = B.reshape(hsvt.shape[:2])


4 - Now apply a convolution with a circular disc, B = D * B, where D is the disc kernel.

disc = cv2.getStructuringElement(cv2.MORPH_ELLIPSE,(5,5))
cv2.filter2D(B,-1,disc,B)
B = np.uint8(B)
cv2.normalize(B,B,0,255,cv2.NORM_MINMAX)


5 - Now the location of maximum intensity gives us the location of object. If we are expecting a region in the image, thresholding for a suitable value gives a nice result.

ret,thresh = cv2.threshold(B,50,255,0)


Below is one example I worked with. I used the region inside blue rectangle as sample object and I wanted to extract all the red roses. See, ROI is filled with red color only :

 Histogram Backprojection

Backprojection in OpenCV

OpenCV provides an inbuilt function cv2.calcBackProject(). Its parameters are almost same as the cv2.calcHist() function. One of its parameter is histogram which is histogram of the object and we have to find it. Also, the object histogram should be normalized before passing on to the backproject function. It returns the probability image. Then we convolve the image with a disc kernel and apply threshold. Below is my code and output :

import cv2
import numpy as np

hsv = cv2.cvtColor(img,cv2.COLOR_BGR2HSV)

hsvt = cv2.cvtColor(target,cv2.COLOR_BGR2HSV)

# calculating object histogram
roihist = cv2.calcHist([hsv],[0, 1], None, [180, 256], [0, 180, 0, 256] )

# normalize histogram and apply backprojection
cv2.normalize(roihist,roihist,0,255,cv2.NORM_MINMAX)
dst = cv2.calcBackProject([hsvt],[0,1],roihist,[0,180,0,256],1)

# Now convolute with circular disc
disc = cv2.getStructuringElement(cv2.MORPH_ELLIPSE,(5,5))
cv2.filter2D(dst,-1,disc,dst)

# threshold and binary AND
ret,thresh = cv2.threshold(dst,50,255,0)
thresh = cv2.merge((thresh,thresh,thresh))
res = cv2.bitwise_and(target,thresh)

res = np.vstack((target,thresh,res))
cv2.imwrite('res.jpg',res)


Below is the output. Here ROI is not just flower, but some green part is also included. Still output is good. On close analysis of the center image, you can see the leaf parts slightly which will be removed on threshold :

 Histogram Backprojection in OpenCV

Summary

So we have looked on what is Histogram backprojection, how to calculate it, how it is useful in object detection etc. It is also used in more advanced object tracking methods like camshift. We will do that later.

Regards,
Abid Rahman K.

References :

1 - "Indexing via color histograms", Swain, Michael J. , Third international conference on computer vision,1990.
2 - http://www.codeproject.com/Articles/35895/Computer-Vision-Applications-with-C-Part-II
3 - http://theiszm.wordpress.com/tag/backprojection/