Color vegetation indices enable various precision agriculture applications by transforming a 3D-color image into its 1D-grayscale counterpart, such that the color of vegetation pixels can be accentuated, while those of nonvegetation pixels are attenuated. The quality of the transformation is essential to the outcomes of computational analyses to follow. The objective of this article is to propose a new vegetation index, the Elliptical Color Index (ECI), which leverages the quadratic discriminant analysis of 3D-color images along a normalized red (r)—green (g) plane. The proposed index is defined as an ellipse function of r and g variables with a shape parameter. For comparison, the ECI’s performance was evaluated along with six other indices, by using 240 color images as a test sample captured from four vegetation species under different illumination and background conditions, together with the corresponding ground-truth patterns. For comparative analysis, the receiver operating characteristic (ROC) and the precision–recall (PR) curves helped quantify the overall performance of vegetation segmentation across all of the vegetation indices evaluated. For a practical appraisal of vegetation segmentation outcomes, this paper applied Gaussian filtering, and then the thresholding method of Otsu, to the grayscale images transformed by each of the indices. Overall, the test results confirmed that ECI outperforms the other indices, in terms of the area under the curves of ROC and PR, as well as other performance metrics, including total error, precision, and F-score.