OBJECTIVE: We used an algorithm for quantitative image processing to classify breast tissue into the categories fibrosis, involution atrophy, and normal. The algorithm entailed use of Minkowski functionals in topologic analysis of x-ray attenuation patterns on digital mammograms. The results were compared with those of techniques based on evaluation of gray-level histograms. MATERIALS AND METHODS: One hundred digital mammograms were classified by consensus of two experienced readers. A topologic parameter extracted from the Minkowski functional spectra was obtained for retromammilar image sections (512 x 512 pixels). From the gray-level histogram of each of these samples, the 20th percentile, median, and mean were determined. Discriminant analysis was used to assess the predictive value of the methods with respect to correct categorization. RESULTS: The mean gray-level intensity of normal breast tissue was 90 +/- 9, and the 20th percentile was 68 +/- 18. The mean gray-level intensity was 84 +/- 7 for involution and 90 +/- 8 for fibrosis; the 20th percentile was 75 +/- 6 for involution and 73 +/- 10 for fibrosis. The results of discriminant analysis showed that use of the gray-level histogram parameters led to correct classification in 66% of cases. Use of topologic analysis with Minkowski functionals increased the rate of correct classification to 83%. When a combined model of histogram-derived parameters and Minkowski functionals was used, 89% of cases were categorized correctly. CONCLUSION: Topologic analysis of x-ray attenuation patterns on digital mammograms obtained with Minkowski functionals is simple and robust, and the results agree with radiologists' ratings. Because correct classification is significantly higher than with use of density features, our technique may be an objective and quantitative alternative in the evaluation of the parenchymal structure of the breast.
OBJECTIVE: We used an algorithm for quantitative image processing to classify breast tissue into the categories fibrosis, involution atrophy, and normal. The algorithm entailed use of Minkowski functionals in topologic analysis of x-ray attenuation patterns on digital mammograms. The results were compared with those of techniques based on evaluation of gray-level histograms. MATERIALS AND METHODS: One hundred digital mammograms were classified by consensus of two experienced readers. A topologic parameter extracted from the Minkowski functional spectra was obtained for retromammilar image sections (512 x 512 pixels). From the gray-level histogram of each of these samples, the 20th percentile, median, and mean were determined. Discriminant analysis was used to assess the predictive value of the methods with respect to correct categorization. RESULTS: The mean gray-level intensity of normal breast tissue was 90 +/- 9, and the 20th percentile was 68 +/- 18. The mean gray-level intensity was 84 +/- 7 for involution and 90 +/- 8 for fibrosis; the 20th percentile was 75 +/- 6 for involution and 73 +/- 10 for fibrosis. The results of discriminant analysis showed that use of the gray-level histogram parameters led to correct classification in 66% of cases. Use of topologic analysis with Minkowski functionals increased the rate of correct classification to 83%. When a combined model of histogram-derived parameters and Minkowski functionals was used, 89% of cases were categorized correctly. CONCLUSION: Topologic analysis of x-ray attenuation patterns on digital mammograms obtained with Minkowski functionals is simple and robust, and the results agree with radiologists' ratings. Because correct classification is significantly higher than with use of density features, our technique may be an objective and quantitative alternative in the evaluation of the parenchymal structure of the breast.