1. Gradient Inverse Coefficient of Variation and Leukocyte Detection Let (X i, Y i ), i=1:n be points on a curve. Let n(X i, Y i ) denote the normal to the curve at (X i, Y i ). Further, let I denote the image. Then gradient inverse coefficient of variation (GICOV) is defined as: We hypothesize that if a closed curve (X i, Y i ) is delineating a leukocyte, the GICOV value will be the highest within a local neighborhood of the curve. GICOV can be utilized in detecting rolling leukocytes from in vivo microscopic video imagery.

2. Leukocyte Detection: Step 1 R x, R y : Radii of ellipse  : Rotation angle of ellipse t : parameter to represent an ellipse point, t  [0,2  ]. Step 1: Select a set of N ellipses by varying radii and orientation. We know the approximate size of a leukocyte; so the range of radii in some discrete step size is always a finite number. Similarly the range of orientation (rotation angle) is also finite. A rotated ellipse defined by three parameters R x, R y and 

3. Leukocyte Detection: Step 2 Step 2: For each pixel location (x, y) in the image, we compute N GICOV values for the N ellipses. We choose the highest value of GICOV and note the corresponding two radii and rotation angle of the ellipse producing the highest GICOV (call this GICOV *). We now compute local maximum of GICOV* values within a circular neighborhood and identify corresponding pixel locations throughout the image, utilizing a circular neighborhood (B) of certain size for every pixel location. This leaves us with a few pixel locations that are potential leukocyte centers. Ellipses corresponding to locally maximum GICOV *

4. Leukocyte Detection: Step 3 Step 3: Relax each ellipse to flexible contours by b-splines. (we will talk more, in fact a lot more about this and related stuff) Yellow contour: ellipse Green contour: B-spline

5. Leukocyte Detection: Step 4 Step 4: Re-compute GICOV on the B-spline and apply Bayes’ classifier to the computed GICOV Final result