Maylor K. H. Leung

Ellipse Detection with Hough Transform in One Dimensional Parametric Space

The main advantage of using the Hough Transform to detect ellipses is its robustness against missing data points. However, the storage and computational requirements of the Hough Transform preclude practical applications. Although there are many modifications to the Hough Transform, these modifications still demand significant storage requirement. In this paper, we present a novel ellipse detection algorithm which retains the original advantages of the Hough Transform while minimizing the storage and computation complexity. More specifically, we use an accumulator that is only one dimensional. As such, our algorithm is more effective in terms of storage requirement. In addition, our algorithm can be easily parallelized to achieve good execution time. Experimental results on both synthetic and real images demonstrate the robustness and effectiveness of our algorithm in which both complete and incomplete ellipses can be extracted.

Polygonal Representation of Digital Curves

Approximating digital curves using polygonal approximations is required in many image processing applications [Kolesnikov & Franti, 2003, 2005; Lavallee & Szeliski, 1995; Leung, 1990; Mokhtarian & Mackworth, 1986; Prasad, et al., 2011; Prasad & Leung, 2010a, 2010b; Prasad & Leung, 2010; Prasad & Leung, 2012; Prasad, et al., 2011a]. Such representation is used for representing noisy digital curves in a more robust manner, reducing the computational resources required for processing and storing them, and for computing various geometrical properties of digital curves. Specifically, properties like curvature estimation, tangent estimation, detecting inflexion points, perimeter of the curves, etc., which are very sensitive to the digitization noise. Polygonal approximation is also useful in topological representation, segmentation and contour feature extraction in the applications of object detection, face detection, etc.

Error Analysis of Geometric Ellipse Detection Methods Due to Quantization

Many geometric methods have been used extensively for detection of ellipses in images. Though the geometric methods have rigorous mathematical framework, the effect of quantization appears in various forms and introduces errors in the implementation of such models. This unexplored aspect of geometric methods is studied in this paper. We identify the various sources that can affect the accuracy of the geometric methods. Our results show that the choice of points used in geometric methods is a very crucial factor in the accuracy. If the curvature covered by the chosen points is low, then the error may be significantly high. We also show that if numerically computed tangents are used in the geometric methods, the accuracy of the methods is sensitive to the error in the computation of the tangents. Our analysis is used to propose a probability density function for the relative error of the geometric methods. Such distribution can be an important tool for determining practical parameters like the size of bins or clusters in the Hough transform. It can also be used to compare various methods and choose a more suitable method.

Methods for Ellipse Detection from Edge Maps of Real Images

Detecting geometric shapes like ellipses from real images have many potential applications. Some examples include pupil tracking, detecting spherical or ellipsoidal objects like fruits, pebbles, golf balls, etc. from a scene for robotic applications, detecting ellipsoidal objects in underwater images, detecting fetal heads, cells, or nuclei in biological and biomedical images, identifying the eddy currents and zones using oceanic images, forming structural descriptors for objects and faces, traffic sign interpretation1, etc.

An error bounded tangent estimator for digitized elliptic curves

In this paper, we address the problem of tangent estimation for digital curves. We propose a simple, geometry based tangent estimation method for digital curves. The geometrical analysis of the method and the maximum error analysis for digital elliptic curves are presented. Numerical results have been tested for digital ellipses of various eccentricities (circle to very sharp ellipses) and the maximum error of the proposed method is bounded and is less than 5.5 degrees for reasonably large ellipses. The error for digital circles is also analyzed and compared with a recent tangent estimation method. In addition, the tangent estimation technique is applied to a flower shaped digital curve with six inflexion points and the results demonstrate good performance. The proposed tangent estimator is applied to a practical application which analyzes the error in a geometric ellipse detection method. The ellipse detection method is greatly benefited by the proposed tangent estimator, as the maximum error in geometrical ellipse detection is no more critically dependent upon the tangent estimation (due to the reduced error in tangent estimation). The proposed tangent estimator also increases the reliability and precision of the ellipse detection method.

Structural Descriptors for Category Level Object Detection

We propose a new class of descriptors which exhibits the ability to yield meaningful structural descriptions of objects. These descriptors are constructed from two types of image primitives: quadrangles and ellipses. The primitives are extracted from an image based on human cognitive psychology and model local parts of objects. Experiments reveal that these primitives densely cover objects in images. In this regard, structural information of an object can be comprehensively described by these primitives. It is found that a combination of simple spatial relationships between primitives plus a small set of geometrical attributes provide rich and accurate local structural descriptions of objects. Category level object detection of four-legged animals, bicycles, and cars images is demonstrated under scaling, moderate viewpoint variations, and background clutter. Promising results are achieved.

A split and merge based ellipse detector

We present an ellipse detector that continually pools lower level information of the edge pixels together to achieve robust detection of the ellipses present in the image. In addition, the parameters of the detected ellipses are continually refined using a close loop system driven by Gestalt psychology. We highlight that we do not rely on the geometrical properties of the ellipses to detect the ellipses. In this aspect, our algorithm is well suited to detect partially occluded ellipses in the image. Experiments on real and synthetic images demonstrate the robustness of our algorithm in which both complete and incomplete ellipses can be detected. In particular, experimental results show that the mean detection accuracy of our algorithm surpasses 92% even with around 90% outliers in the images. This detection performance is superior to that achieved by the robust regression, least squares and the hough transform based ellipse detectors.

Reliability / precision uncertainity in shape fitting problems

The precision/uncertainty duality has been long known in the context of Hough transform, where a shape in an image cannot be fit precisely using the Hough transform without compromising the certainty or reliability of the fitting. This paper mathematically shows that such duality also exists while using the least squares based method. This paper also proposes a method to quantify the reliability of a fit. Further, based on the proposed measure of reliability, an optimization scheme to strike a balance between the precision and reliability is suggested. Though the mathematical formulations deal with only straight line, considering it as the simplest and basic geometric primitive, it is argued that such duality exists for any shape fitting and applies to any shape fitting method.

Object Class Recognition using Quadrangles

We present a new class of human psychology inspired descriptors that exhibits the ability to yield meaningful structural descriptions of an object. Our framework involves (1) detecting salient pairings of lines segments which are extracted from the line edge map of an image and (2) exploiting these pairs of line segments to construct the structural descriptors. Specifically, we integrate the spatial qualities of the line segments with the perceptually salient colors of the image to jointly identify the salient pairings of the line segments. We term such pairings of line segments as the quadrangles. By harnessing the spatial configurations and the geometrical relationships between the quadrangles, we design descriptors which characterize the local structures of an object. Promising recognition results of the four-legged animals are presented.