This work proposes a novel, model-based, computer vision method for recognizing planar biological shapes. The coordinate functions of the contours of the objects to be recognized are convolved with Gaussian kernels to evolve them in scale-space, and are used as representations of shape. A new technique for calculating curvature was developed in this work. This technique does not require parametrized coordinate functions and does not amplify noise. Invariance of curvature to uniform scaling, rotation and translation are used to advantage. The scale up to which contours are evolved is determined from the analysis of the power spectrum of the coordinate functions of the contours at scale zero and using the scaling property of the scale-space representation. An adaptation of the contour limiting technique was used for building models that accept adjustable variability, based on the point by point variance of an ensemble of curvature functions. Also, the notion of conceptual models was introduced. To show the usefulness of the method with real data, it was applied to recognize a specific type of corneal cells whose shape is used as an index of acceptable quality of corneal tissue for transplantation, as well as for other ophthalmologic evaluations