In this paper, we propose a robust and accurate method to detect fingertips of hand palm with a down-looking camera mounted on an eyeglass for the utilization of hand gestures for user interaction between human and computers. To ensure consistent performance under unconstrained environments, we propose a novel method to precisely locate fingertips by combing both statistical information of palm edge distribution and structure information of convex null analysis on palm contour. Briefly, first SVM (support vector machine) with a statistical nine-bin based HOG (histogram of oriented gradient) features is introduced for robust hand detection from video stream. Then, binary image regions are segmented out by an adaptive Cg-Cr model on detected hands. With the prior information of hand contour, it takes a global optimization approach of convex hull analysis to locate hand fingertip. The experimental results have demonstrated that the proposed approach performs well because it can well detect all hand fingertips even under some extreme environments.