Leaf recognition for accurate plant classification.

Doctor of Philosophy in Computer Science, University of KwaZulu-Natal, Durban 2017.Plants are the most important living organisms on our planet because they are sources of energy and protect our planet against global warming. Botanists were the first scientist to design techniques for plant species recognition using leaves. Although many techniques for plant recognition using leaf images have been proposed in the literature, the precision and the quality of feature descriptors for shape, texture, and color remain the major challenges. This thesis investigates the precision of geometric shape features extraction and improved the determination of the Minimum Bounding Rectangle (MBR). The comparison of the proposed improved MBR determination method to Chaudhuri's method is performed using Mean Absolute Error (MAE) generated by each method on each edge point of the MBR. On the top left point of the determined MBR, Chaudhuri's method has the MAE value of 26.37 and the proposed method has the MAE value of 8.14. This thesis also investigates the use of the Convexity Measure of Polygons for the characterization of the degree of convexity of a given leaf shape. Promising results are obtained when using the Convexity Measure of Polygons combined with other geometric features to characterize leave images, and a classification rate of 92% was obtained with a Multilayer Perceptron Neural Network classifier. After observing the limitations of the Convexity Measure of Polygons, a new shape feature called Convexity Moments of Polygons is presented in this thesis. This new feature has the invariant properties of the Convexity Measure of Polygons, but is more precise because it uses more than one value to characterize the degree of convexity of a given shape. Promising results are obtained when using the Convexity Moments of Polygons combined with other geometric features to characterize the leaf images and a classification rate of 95% was obtained with the Multilayer Perceptron Neural Network classifier. Leaf boundaries carry valuable information that can be used to distinguish between plant species. In this thesis, a new boundary-based shape characterization method called Sinuosity Coefficients is proposed. This method has been used in many fields of science like Geography to describe rivers meandering. The Sinuosity Coefficients is scale and translation invariant. Promising results are obtained when using Sinuosity Coefficients combined with other geometric features to characterize the leaf images, a classification rate of 80% was obtained with the Multilayer Perceptron Neural Network classifier. Finally, this thesis implements a model for plant classification using leaf images, where an input leaf image is described using the Convexity Moments, the Sinuosity Coefficients and the geometric features to generate a feature vector for the recognition of plant species using a Radial Basis Neural Network. With the model designed and implemented the overall classification rate of 97% was obtained

A measure of non-convexity in the plane and the Minkowski sum

In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for "not far from convex" regions this measure does not decrease under the Minkowski sum operation, and guarantees that the Minkowski sum has no "holes".Comment: 5 figures; Discrete and Computational Geometry, 201

Automatic Image Registration in Infrared-Visible Videos using Polygon Vertices

In this paper, an automatic method is proposed to perform image registration in visible and infrared pair of video sequences for multiple targets. In multimodal image analysis like image fusion systems, color and IR sensors are placed close to each other and capture a same scene simultaneously, but the videos are not properly aligned by default because of different fields of view, image capturing information, working principle and other camera specifications. Because the scenes are usually not planar, alignment needs to be performed continuously by extracting relevant common information. In this paper, we approximate the shape of the targets by polygons and use affine transformation for aligning the two video sequences. After background subtraction, keypoints on the contour of the foreground blobs are detected using DCE (Discrete Curve Evolution)technique. These keypoints are then described by the local shape at each point of the obtained polygon. The keypoints are matched based on the convexity of polygon's vertices and Euclidean distance between them. Only good matches for each local shape polygon in a frame, are kept. To achieve a global affine transformation that maximises the overlapping of infrared and visible foreground pixels, the matched keypoints of each local shape polygon are stored temporally in a buffer for a few number of frames. The matrix is evaluated at each frame using the temporal buffer and the best matrix is selected, based on an overlapping ratio criterion. Our experimental results demonstrate that this method can provide highly accurate registered images and that we outperform a previous related method

Polygons as optimal shapes with convexity constraint

In this paper, we focus on the following general shape optimization problem: \min\{J(\Om), \Om convex, \Om\in\mathcal S_{ad}\}, where $\mathcal S_{ad}$ is a set of 2-dimensional admissible shapes and $J:\mathcal{S}_{ad}\to\R$ is a shape functional. Using a specific parameterization of the set of convex domains, we derive some extremality conditions (first and second order) for this kind of problem. Moreover, we use these optimality conditions to prove that, for a large class of functionals (satisfying a concavity like property), any solution to this shape optimization problem is a polygon

Moduli spaces of toric manifolds

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance is related to the Duistermaat-Heckman measure and the Hausdorff metric. While the moduli space, its topology and metric, may be constructed in any dimension, the tools we use in the proofs are four-dimensional, and hence so is our main result.Comment: To appear in Geometriae Dedicata, minor changes to previous version, 19 pages, 6 figure