An ellipse rotating in the image plane can produce several different percepts. The two-dimensional (2D) percepts are either a rotating rigid ellipse or a constantly deforming non-rigid ellipse. The 3D percept is a rotating rigid circular disk that is tilted relative to the image plane. Stimuli that generate 3D percepts based on purely 2D rotational motion are known as stereokinetic stimuli. We ...

Fisher's geometrical model was introduced to study the phenotypic size of mutations contributing to adaptation. However, as pointed out by Haldane, the model involves a simplified picture of the action of natural selection, and this calls into question its generality. In particular, Fisher's model assumes that each trait contributes independently to fitness. Here, we show that Haldane's concern...

We study the problem of fitting ellipses to observed points in the context of Errors-In-Variables regression analysis. The accuracy of fitting methods is characterized by their variances and biases. The variance has a theoretical lower bound (the KCR bound), and many practical fits attend it, so they are optimal in this sense. There is no lower bound on the bias, though, and in fact our higher ...

Many biological and astronomical forms can be best represented by ellipses. While some more complex curves might represent the shape more accurately, ellipses have the advantage that they are easily parameterised and define the location, orientation and dimensions of the data more clearly. In this paper, we present a method of direct least-squares ellipse fitting by solving a generalised eigens...

This algorithm draws ellipses with integer centres and decimal radii on discrete devices using fixed-point arithmetic. These ellipses have both X and Y axis parallel to the coordinate axes. It uses forward differences to diminish its cost. It has a low comp utational complexity while the error is lower than traditional algorithms. This algorithm works in the squared R space (fixed-point) and tr...

Our fully automatic method to compute the biparietal diameter (BPD) and occipitofrontal diameter (OFD) from fetal ultrasound images is based on fitting an ellipse modelling the head contour of the fetus to ultrasound images. This is achieved by minimizing a cost function with respect to the parameters of the ellipse using a global multiscale multistart Nelder-Mead algorithm.

In this article, we establish new fixed ellipse theorems that will provide a geometrical perspective to the classical metric point theory. Also, novel consequences as expanding of some existing and known circle in literature case, give non-trivial illuminating examples, which show impressiveness our results. On other hand, using given ellipse, solutions for open question is posed by Rhoades wit...