5. Finally multiply the results all together ( r1 x r2 x r3 )
The result (r) of a cross correlation calculation lies between -1 and +1. If the value is +1 in average the two images are identical. If it is -1 then the images are identical but the image looks like a photographic negative version of the probe image. If r=0 then the images are on average very unlike each other.
People who are interested in Computer Vision are likely to be familiar with the
OpenCV library. The following code snippet (incomplete) is an example for calculating the cross correlation co-efficiency using the OpenCV library in C.
//split img1 in to RGB channels and store them in seperate images
cvSplit(img1, img1R, img1G, img1B, NULL);
//calculate histograms of the the image
CvHistogram *h1R = calHistogram(img1R, bins, ranges);
CvHistogram *h1G = calHistogram(img1G, bins, ranges);
CvHistogram *h1B = calHistogram(img1B, bins, ranges);
//split the image two in to RGB channels and store them
//in seperate images
cvSplit(img2, img2B, img2G, img2R,0);
//calculate histograms of the RGB channel images of the "img2"
CvHistogram *h2R = calHistogram(img2R, bins, ranges);
CvHistogram *h2G = calHistogram(img2G, bins, ranges);
CvHistogram *h2B = calHistogram(img2B, bins, ranges);
//Calculate the correlation coefficient of RGB images, of img1 and img2
rR = cvCompareHist(h1R,h2R,CV_COMP_CORREL);
rG = cvCompareHist(h1G,h2G,CV_COMP_CORREL);
rB = cvCompareHist(h1B,h2B,CV_COMP_CORREL);
//Multiply the results together
tempR= rR*rG*rB;
The performance:
Some performance evaluation has been done on this program using a test harness called 'Fact'.
Error rates calculated from mycbir
tests TP TN FP FN accuracy recall precision specificity class
8 0 0 8 0 0.00 0.00 0.00 0.00 box
8 0 0 8 0 0.00 0.00 0.00 0.00 cockeral
8 6 0 2 0 0.75 1.00 0.75 0.00 dog
9 7 0 2 0 0.78 1.00 0.78 0.00 horus
8 7 0 1 0 0.88 1.00 0.88 0.00 ornament
10 8 0 2 0 0.80 1.00 0.80 0.00 penguin
8 1 0 7 0 0.12 1.00 0.12 0.00 reindeer
9 2 0 7 0 0.22 1.00 0.22 0.00 tortoise
68 31 0 37 0 0.46 1.00 0.46 0.00 overall
TP = True Positives
TN= True Negatives
FP = False Positives
FN= False Negatives
In the matrix above it shows the amount of test cases for the each picture in the “test” column, True Positives, True Negatives, False Positives and False Negatives in the next four columns. Then the application calculates the accuracy, recall, precision and specificity as follows, and displays in the next four columns. The last “class” column show the type of picture that it has carried out the test on,
Precision is the number of relevant pictures that are retrieved, divided by the total number of of pictures retrieved. Recall is the number of relevant pictures retrieved divided by the total existing relevant pictures. The specificity and the accuracy is calculated as below
TP TN
sensitivity = recall = ------------------ specificity = -----------------
TP + TN FP + TN
As you can see above, the application has failed to find the True
Positives for the “box” and “cockeral” pictures. So in
contrast it has found False Positives in all cases. The best case is
the tests on the ornament pictures as it has found 7/8 TPs and 1/8
FPs. Overall this algorithm has done 68 test cases and have found 31
True Positives and 37 False Positives, but no True Negatives or False
Negatives.
The matrix below, is the class confusion matrix.
Confusion matrix calculated from mycbir
expected
actual box cockeral dog horus ornament penguin reindeer tortoise
box 0 0 0 0 0 0 0 1
dog 0 0 6 0 0 0 0 0
horus 0 0 1 7 0 0 0 4
ornament 1 1 0 0 7 2 7 0
penguin 1 0 0 0 1 8 0 0
reindeer 5 7 0 1 0 0 1 2
tortoise 1 0 1 1 0 0 0 2
The columns and rows indicates that, the classes in the rows titles
were obtained when the classes in the column title should have been
found (Rows as obtained results, columns as expected result). The
numbers indicates the number of times it has been obtained. So as an
example, as the worst case: in the “box” column,
ornament =1, penguin = 1, reindeer = 5, tortoise = 1 has been
obtained when “box” pictures should have been found. But it has
not obtained any “box” pictures as the value of the “box” raw
is 0.
As I have mentioned earlier the best results has been obtained on the
tests with the “ornament” picture. It has obtained the correct
“ornament” pictures 7 times and a penguin picture just one time.
Conclusion:
Cross correlation is not the best Content based Image Retrieval technique to date, though it helps us to understand how the histograms of two images can vary or can be complementary. But it is no doubt that analysing just the colours in images are a good way of characterising them though it is hard to compare two images using just this factor.
