Geometric information is omnipresent in any data used as input in computer graphics applications. While this is obvious for geometry processing applications, where 3D models are the objects of interest, it is not directly apparent in the case of image and video processing applications. However, there are at least two different views for interpreting images as representations for geometric information. First, images can be seen as height fields over spatial 2D domains and as such describe geometric shapes in the used color space. Second, images show projected 3D geometry, which we can describe or at least approximate and exploit. In order to take advantage of the provided geometric information in the input data the key issue is to find the most appropriate geometry representation which is perfectly suited for specific application's requirements.In this thesis we show that a combination of raster- and vector-representations of the geometric information contained in the input data provides novel opportunities and ways for solving very challenging tasks in the areas of image and geometry processing. By this we also draw parallels between these two, at first glance, completely different areas in computer graphics, and show a way to address problems posed in these areas in a unified manner. We present a number of novel approaches which provide several improvements over previous works by appropriate recovery and exploitation of different geometry representations in the input data.