Image texture is a very important component in many types of images, including medical images. Medical images are often corrupted by noise and affected by artifacts. Some of the texture-based features that should describe the structure of the tissue under examination may also reflect, for example, the uneven sensitivity of the scanner within the tissue region. This in turn may lead to an inappropriate description of the tissue or incorrect classification. To limit these phenomena, the analyzed regions of interest are normalized. In texture analysis methods, image intensity normalization is usually followed by a reduction in the number of levels coding the intensity. The aim of this work was to analyze the impact of different image normalization methods and the number of intensity levels on texture classification, taking into account noise and artifacts related to uneven background brightness distribution. Analyses were performed on four sets of images: modified Brodatz textures, kidney images obtained by means of dynamic contrast-enhanced magnetic resonance imaging, shoulder images acquired as T2-weighted magnetic resonance images and CT heart and thorax images. The results will be of use for choosing a particular method of image normalization, based on the types of noise and distortion present in the images.