The Haralick texture features are common in the image analysis literature, partly because of their simplicity and because their values can be interpreted. It was recently observed that the Haralick texture features are very sensitive to the size of the GLCM that was used to compute them, which led to a new formulation that is invariant to the GLCM size. However, these new features still depend on the sample size used to compute the GLCM, i.e. the size of the input image region-of-interest (ROI).The purpose of this work was to investigate the performance of density estimation methods for approximating the GLCM and subsequently the corresponding invariant features.Three density estimation methods were evaluated, namely a piece-wise constant distribution, the Parzen-windows method, and the Gaussian mixture model. The methods were evaluated on 29 different image textures and 20 invariant Haralick texture features as well as a wide range of different ROI sizes.The results indicate that there are two types of features: those that have a clear minimum error for a particular GLCM size for each ROI size, and those whose error decreases monotonically with increased GLCM size. For the first type of features, the Gaussian mixture model gave the smallest errors, and in particular for small ROI sizes (less than about 20×20).In conclusion, the Gaussian mixture model is the preferred method for the first type of features (in particular for small ROIs). For the second type of features, simply using a large GLCM size is preferred.