Evolute‐based Hough transform method for characterization of ellipsoids

Abstract

SummaryWe propose a novel and algorithmically simple Hough transform method that exploits the geometric properties of ellipses to enable the robust determination of the ellipse position and properties. We make use of the unique features of the evolute created by Hough voting along the gradient vectors of a two-dimensional image to determine the ellipse centre, orientation and aspect ratio. A second one-dimensional voting is performed on the minor axis to uniquely determine the ellipse size. This reduction of search space substantially simplifies the algorithmic complexity. To demonstrate the accuracy of our method, we present analysis of single and multiple ellipsoidal particles, including polydisperse and imperfect ellipsoids, in both simulated images and electron micrographs. Given its mathematical simplicity, ease of implementation and reasonable algorithmic completion time, we anticipate that the proposed method will be broadly useful for image processing of ellipsoidal particles, including their detection and tracking for studies of colloidal suspensions, and for applications to drug delivery and microrheology.

Automatic Biological Cell Counting Using a Modified Gradient Hough Transform

“…We do this by using the information from the merged LCL of the V ( i , j ). We can therefore compute a radial and an angular histogram as described in Kierkegaard (1992) and determine the radii of the circles, even those which are concentric or fragmented.…”

“…In order to improve the automation of cell counting, we suggest modification of the Gradient Accumulation Transform (GAT) method presented by Kierkegaard (1992) and used by Kaytanli & Valentine (2013). This method is based on three ideas.…”

“…Gradients were also used in an iterative method to determine the centers of circles in semi-conductor images (Timm & Barth, 2011). In Kierkegaard (1992), the author gave a clear definition of the so-called gradient accumulation method. Most of these Circular Hough Transform (CHT) methods use common steps.…”

“…Our algorithm is mainly based on the accumulation of gradients, as described in Kierkegaard (1992) and Timm & Barth (2011). The first modification that we introduce is the use of a first-order derivative of a two-dimensional (2D) Gaussian distribution, instead of the Sobel filter.…”