This paper presents an eye detection technique basedon color and shape features. The approach consists of three steps: a rough eye localization using projection technique, a white color thresholding to extract white sclera, and an ellipse fitting to fit the ellipse shape of eye. The proposed white color thresholding utilizes the normalized RGB chromaticty diagram, where white color objects are ...

Caustics are curves with the property that a billiard trajectory, once tangent to it, stays tangent after every reflection at the boundary of the billiard table. When the billiard table is an ellipse, any nonsingular billiard trajectory has a caustic, which can be either a confocal ellipse or a confocal hyperbola. Resonant caustics —the ones whose tangent trajectories are closed polygons— are d...

In this work we present a technique for tracking contours from echocardiogram video. Our aim is to calculate area of a heart chamber, say, left ventricle(LV), over time from the video. To do so, we have tried to estimate LV boundary by an ellipse for each frame. The system requires a user drawn ellipse describing the LV in the rst frame. For the next frames, this ellipse is adjusted according t...

-In this paper we use the parameteric polar representation to extend the application of edge directional information from circle to ellipse extraction. As a result we obtain a mapping which decomposes the parameter space required for ellipse extraction into two independent sub-spaces and one final histogram accumulator. The mapping includes the tangent of the angle of the first and second direc...

An elliptical region of the plane supports a positive-valued function whose Radon transform depends only on the slope of the integrating line. Any two parallel lines that intersect the ellipse generate equal line integrals of the function. We prove that this peculiar property is unique to the ellipse; no other convex, compact region of the plane supports a nonzero-valued function whose Radon tr...