Multiple ellipse fitting is challenging and at the same time essential as it has a variety of applications in biology, chemistry, and nanotechnology. Accurate, effective, and reliable approach for the fitting problem has been always desirable. In this paper, we address a category of multiple ellipse fitting problem which fits densely connected contours. We propose a framework rather than design an algorithm for the problem. The framework streamlines five processes which include: sorting the contour points, doing ellipse fitting in sliding windows, detecting the context anomaly, performing clustering, and obtaining multiple ellipses through second ellipse fitting. The framework is evaluated in a real-world application of handprint identification and various synthetic datasets. Experimental results show that the framework can extract multiple ellipses from contours with satisfactory accuracy and efficiency.