An improved technique for fractal characterization called the modified blanket method is introduced that can quantify surrounding fractal structures on a pixel by pixel basis without artifacts associated with scale-dependent image features such as object size. The method interprets images as topographical maps, obtaining information regarding the local surface area as a function of image resolution. Local fractal dimension (FD) can be quantified from the power law exponent derived from the surface area and image resolution relationship. We apply this technique on simulated cell images of known FD and compared the obtained values to power spectral density (PSD) analysis. Our method is sensitive to a wider FD range (2.0-4.5), having a mean error of 1.4% compared to 6% for PSD analysis. This increased sensitivity and an ability to compute regional FD properties enabled the discrimination of the differences in radiation resistant cancer cell responses that could not be detected using PSD analysis.