An image analysis method called two-dimensional wavelet packet analysis (2D WPA) is introduced to quantify branching complexity of neurons. Both binary silhouettes and contour profiles of neurons were analyzed to determine accuracy and precision of the fractal dimension in cell classification tasks. Two-dimensional WPA plotted the slope of decay for a sorted list of discrete wavelet packet coefficients belonging to the adapted wavelet best basis to obtain the fractal dimension for test images and binary representations of neurons. Two-dimensional WPA was compared with box counting and mass-radius algorithms. The results for 2D WPA showed that it could differentiate between neural branching complexity in cells of different type in agreement with accepted methods. The importance of the 2D WPA method is that it performs multiresolution decomposition in the horizontal, vertical, and diagonal orientations.