Entropy Thresholding is a means of thresholding an image that selects an optimum threshold value by choosing the pixel intensity from the image's histogram that exhibits the maximum entropy over the entire image.
Algorithm[]
C++ code[]
ImageSpace ImageSpace::EntropyThreshold(void)
{
ImageSpace *ReturnImageSpace = new ImageSpace;
BYTE *b1 = new BYTE[ XMax*YMax ];
int ThresholdLevel, *hist;
double prob[256], Sum_prob_1k = 0, Sum_prob_kl = 0,
Sum_prob_ln_1k = 0, Sum_prob_ln_kl = 0, Entropy[256];
//gets histogram of image
hist = Histogram();
// probability distribution
for( int i = 0; i< 256; i++)
prob[i] = (double) hist[i] / (XMax * YMax);
// k is trial threshold level
for( int k = 0; k< 255; k++)
{
Sum_prob_1k = 0; Sum_prob_kl = 0;
Sum_prob_ln_1k = 0; Sum_prob_ln_kl = 0;
//From 1 to k
for(i = 1; i < k; i++)
{
//Sums probablities to k
Sum_prob_1k += prob[i];
//Sums prob times Log of prob to k
if(prob[i]!=0) Sum_prob_ln_1k += (prob[i] * log(prob[i]));
}
for(i = k; i < 256; i++)
//From k to end
{
//Sums prob of k to end
Sum_prob_kl += prob[i];
//Sums prob times log of prob
if(prob[i]!=0) Sum_prob_ln_kl += (prob[i] * log(prob[i]));
}
//Final equation of entropy for each k
Entropy[k] = log(Sum_prob_1k) + log(Sum_prob_kl)
- (Sum_prob_ln_1k / Sum_prob_1k)
- (Sum_prob_ln_kl / Sum_prob_kl);
//protects against divide by zero
if(Entropy[k]<0) Entropy[k]=0;
}
ThresholdLevel = 0;
for(k = 0; k<256; k++) //Finds Maximum
if(Entropy[k] > Entropy[ThresholdLevel]) ThresholdLevel = k;
//Thresholds there
cout << "Thresholded at :" << ThresholdLevel << endl;
for( int y=0; y < YMax; y++ ) for( int x=0; x < XMax; x++ )
b1[ x + y * XMax ] = ( b0[ x + y * XMax ] > ThresholdLevel ) ? 255 : 0;
ReturnImageSpace->Load(b1);
IsThreshold = TRUE;
return *ReturnImageSpace;
}