This paper presents a novel feature descriptor and classification algorithms for automated scoring of HER2 in Whole Slide Images (WSI). Since a large amount of processing is involved in analyzing WSI images, the primary design goal has been to keep the computational complexity to the minimum possible level. We propose an efficient method based on characteristic curves which encode all relevant information in a smooth polynomial curve with the percentage of stained membranes plotted against variations in intensity/saturation of the colour thresholds used for segmentation. Our algorithm performed exceedingly well at a recent online contest held by the University of Warwick [1], obtaining the second best points score of 390 out of 420 and the overall seventh position in the combined leaderboard [2]. The paper describes three classification algorithms with features extracted from characteristic curves and provides experimental results and comparative analysis