A polygonization‐based method is used to estimate the fractal dimension and several new scalar lacunarity features from digitized transmission electron micrographs (TEM) of mouse liver cell nuclei. The fractal features have been estimated in different segments of 1D curves obtained by scanning the 2D cell nuclei in a spiral‐like fashion called “peel‐off scanning”. This is a venue to separate estimates of fractal features in the center and periphery of a cell nucleus. Our aim was to see if a small set of fractal features could discriminate between samples from normal liver, hyperplastic nodules and hepatocellular carcinomas. The Bhattacharyya distance was used to evaluate the features. Bayesian classification with pooled covariance matrix and equal prior probabilities was used as the rule for classification. Several single fractal features estimated from the periphery of the cell nuclei discriminated samples from the hyperplastic nodules and hepatocellular carcinomas from normal ones. The outer 25–30% of the cell nuclei contained important texture information about the differences between the classes. The polygonization‐based method was also used as an analysis tool to relate the differences between the classes to differences in the chromatin structure.