Dear Editor: I would like to congratulate the authors for the article regarding the calculation of the so-called ellipse area [1]. As the authors indicated, the algorithms employed to calculate the area of the 95% prediction ellipse using the chi-square or the Rayleigh distribution are in fact only exact when the number of samples of the bivariate variable tends to infinite (when each univariat...

We deduce some approximate formulas for the distance evaluation problem between a point and an ellipse in IR2 and a point and an ellipsoid in IR3. The proposed approach is based on the analytical representation of the distance function as a zero of an appropriate univariate algebraic equation. Key–Words: Distance, point-to-ellipse, point-to-ellipsoid

In this paper, we describe a new approach for estimating and tracking three-dimensional (3D) pose of a human face from the face images obtained from a single monocular view with full perspective projection. We assume that the shape of a 3D face can be approximated by an ellipse and that the aspect ratio of 3D face ellipse is given. Given a monocular image of a face, we ®rst perform an ellipse d...

The establishment of appropriate connectivity in the developing nervous system depends on many molecular guidance cues. A key method for studying the response of nerve fibers to such guidance cues is to culture explants of neural tissue in three-dimensional collagen gels. However, most previous analyses of the neurite outgrowth patterns from these explants have been very simple, often measuring...

Using fMRI we investigated the neural basis of audio-visual processing of speech and non-speech stimuli using physically similar auditory stimuli (speech and sinusoidal tones) and visual stimuli (animated circles and ellipses). Relative to uni-modal stimuli, the different multi-modal stimuli showed increased activation in largely non-overlapping areas. Ellipse-Speech, which most resembles natur...

We prove that there exists a unique ellipse of minimal eccentricity, EI , inscribed in a parallelogram, Ð. We also prove that the smallest nonnegative angle between equal conjugate diameters of EI equals the smallest nonnegative angle between the diagonals of Ð. We also prove that if EM is the unique ellipse inscribed in a rectangle, R, which is tangent at the midpoints of the sides of R, then ...

If T : C∪{∞} → C∪{∞} is a Möbius transformation of the extended complex plane, it is well-known that the image under T of a line or circle is another line or circle. It seems natural to consider the image T (E) of a non-circular ellipse E ⊆ C, although as shown in Figure 1, such a curve is not always an ellipse. For the sake of convenience, we will call a curve C a “möte,” for “Möbius Transform...

-A method is presented to solve for the three-dimensional (3D) object position and orientation from single two-dimensional (2D) images based on a systematic hierarchy of features: primitive features, generalized features, and compound structures. A virtual viewpoint analysis shows that a featurecentered coordinate system allows us to drastically reduce the mathematical complexity of the inverse...

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortestpossible support subject to some design constraints to maximize efficiency. While the resulting snakes are versatile enough to provide a good approximation of any closed curve in the plane, their most important feature is...