Effects of image resolution and noise on estimating the fractal dimension of tissue specimens.

Objective: To investigate the effects of imaging system noise and resolution on the ability to estimate and distinguish relative differences in the fractal dimension of tissue specimens.

Study design: Mathematically derived test images of known fractal dimension mimicking the complexity of epithelial morphology were created. The box-counting method was used to compute fractal dimension. To study the effects of resolution on fractal dimension, the test images were convolved with Gaussian point spread functions (PSF), and effects of noise were studied by adding Poisson and Gaussian noise. Application of these findings was illustrated by measuring the resolution and noise for a typical optical microscope and digital camera (OMDC) system.

Results: Poor spatial resolution reduces the fractal dimension and has an increased adverse effect on higher dimensions. Fractal dimension can be estimated within 7% of the true dimension, and relative differences of 0.1 between dimensions are distinguishable provided the PSF of an imaging system has a full-width-at-half-maximum < or = 4 pixels and the contrast-to-noise ratio > 15. These conditions were satisfied by our OMDC.

Conclusion: Effects of noise and resolution from a typical OMDC system do not significantly inhibit the ability to estimate and distinguish relative differences in the fractal dimension of tissue specimens.