In recent years the use of local characteristics has become one of the dominant approaches to content based object recognition. The detection of interest points is the first step in the process of matching or recognition. A local approach significantly improves and accelerates image retrieval from databases. Therefore a reliable algorithm for feature detection is crucial for many applications. In this thesis we propose a novel approach for detecting characteristic points in an image. Our approach is invariant to geometric and photometric transformations, which frequently appear between scenes viewed in different conditions. We emphasize the problem of invariance to affine transformations. This transformation is particularly important as it can locally approximate the perspective deformations. Previous approaches provide partial solutions to this problem, as not all essential parameters of local features are estimated in an affine invariant way. Our method is truly invariant to affine transformations, which include significant scale changes. An image is represented by a set of extracted points. The interest points are characterized by descriptors, which are computed with local derivatives of the neighborhoods of points. These descriptors together with a similarity measure enable point-to-point correspondences to be established, and as a result, the geometry between images to be computed. In the context of an image database, the descriptors are used to find similar points in the database, and therefore the similar image. The usefulness of our method is confirmed by excellent results for matching and image retrieval. Several comparative evaluations show that our approach provided for larger progress in the context of these applications. In our experiments we use a large set of real images, enabling representative results to be obtained.