Color images are converted to grayscale images. Luminance is typically computed as a weighed sum of the color components. The most often used weights were originally developed for encoding analog color television signals as:

I i = 0 . 299 × R i + 0 . 587 × G i + 0 . 144 × B i ,

where _{R i} , _{G i} and _{B i} are the intensity levels of the red, green, and blue channels of the ^{i th} pixel respectively. Figures 2(a) and 2(b) show a sample color image of the mosquitoes’ eggs and its resulting grayscale version.

As shown in Figure 2(b), the eggs and debris are the dark objects on the white paper. Therefore, a proper binary map of the image can be used to distinguish them from the background. This binary map is defined as:

B i = 1 , if I i ≥ T auto 0 , otherwise.

Where _{B i} and _{I i} are the binary value and intensity of the ^{i th} pixel respectively and _Tautois the automatic threshold value based on an entropic thresholding method proposed in 22 as:

arg max T C B ( T ) + C F ( T ) ,

with

C B ( T ) = − log ∑ g = 0 T p ( g ) p ( T ) 2 ,

and

C F ( T ) = − log ∑ g = T + 1 T ″ p ( g ) 1 − p ( T ) 2 .

Where _Tauto is the value of T that makes _{C B} (T) + _{C F} (T) maximum, p(g) is the probability of intensity level g and p(T) is the cumulative probability function. Unlike the original method 22 , here T ″ controls the maximum value of threshold in order to remove high exposure in the images caused by flash where empirically T ″ ∈ [ 160 , 180 ] . Figure 2(c) shows the resulting binary map of the sample image. As it is shown eggs and debris are properly extracted, after the automatic threshold is found.

In this step eggs and debris are detected by extracting eight-connected neighborhood components. Putting it simply, connected component labeling is the process of assigning labels to the foreground elements in such a way that adjacent foreground elements are assigned to the same label 23 . Here, adjacent means 8-adjacent pixels neighborhood.

Usually, a single mosquito egg has an elongated ellipse shape, while a pile of eggs looks more circular (see Figure 2(b)). Therefore, the eccentricity of the object is used to distinguish single eggs from the piles of eggs. Eccentricity measures how much an object deviates from being circular. It is the ratio of the distance between the foci and its major axis length 24 , defined as:

e = 1 − λ 1 λ 2 ,

λ i = μ ″ 20 + μ ″ 02 2 ± 4 μ ″ 11 + ( μ ″ 20 − μ ″ 02 ) 2 2 .

Where μ ″ mn is the central moment of order (m n), defined as:

μ mn ″ = ∑ u , v ∈ R u − x ̄ p v − x ̄ q ,

where x ̄ , y ̄ is the centroid of the object and u , v ∈ R represents whole set of pixel coordinates inside the object. The value of the eccentricity falls in the interval [0,1]. A value of one indicates a perfect circle and zero indicates a line segment. In this step, the objects with high eccentricity, _e1<e< _e2, are selected as eggs. Values of _{e1 e2}can be set from 0.95 up to 0.99. Experimental results show that more than 80% of the components containing one egg are in this range. Finally, the mode of the size of the candidate objects is chosen as the estimated size for one egg.

Debris are black regions extracted on the binary map (see Figure 2(b) and 2(c)) that could be assessed as eggs on the binary map. Nevertheless, a yellow brownish area often presents around the regions of debris (see Figure 2(a)) that can be used to detect debris. For extracting the brownish area near the debris, a chroma value for each pixel is defined as:

C i = max ( R i , G i , B i ) − min ( R i , G i , B i ) .

In this step, the objects that have at least X pixels with C> _{C E} in their radii r are considered as debris. Parameter _{C E} is 0.15 by default, but the application allows the user to tune it, resulting in a change of the detection sensitivity. Because eggs have a dark color and the paper is white, the rate of true negatives (considering non-debris areas as debris) is negligible and it only happens for the eggs that are inside the yellow brownish area.

The number of the eggs N inside the object i, is estimated as:

N ( i ) = ∥ A ( i ) S ∥ , A ( i ) ≤ 2 × S ∥ A ( i ) × C S ∥ , otherwise,

where A(i) is the area of the object, S is the estimated size of one egg, ∥.∥ is the round function and C is the accumulative ratio which should be less than one. The accumulative ratio is necessary due to the fact that regions in the intersection of the eggs inside a pile are shadowed by the eggs and are usually considered as a connected object in the binary map. Therefore, multiplying by this ratio allows better estimation of the number of eggs.

It should be mentioned that thresholding may produce noise, especially in the grid lines of the paper. There are many methods for noise reduction such as low-pass filters and other smoothing operators. However, these methods highly depend on the size of the filter. Here components smaller than half of the estimated size of one egg, are considered as noise in the Equation (10), and are removed.