Scale and affine-invariant local features have shown excellent performance in image matching, object and texture recognition. This paper optimizes keypoint detection to achieve stable local descriptors, and therefore, an improved image representation. The technique performs scale selection based on a region descriptor, here SIFT, and chooses regions for which this descriptor is maximally stable. Maximal stability is obtained, when the difference between descriptors extracted for consecutive scales reaches a minimum. This scale selection technique is applied to multi-scale Harris and Laplacian points. Affine invariance is achieved by an integrated affine adaptation process based on the second moment matrix. An experimental evaluation compares our detectors to Harris-Laplace and the Laplacian in the context of image matching as well as of category and texture classification. The comparison shows the improved performance of our detector.