Skip to Main content Skip to Navigation
New interface
Journal articles

Wavelet-based 3D reconstruction of microcalcification clusters from two mammographic views: new evidence that fractal tumors are malignant and Euclidean tumors are benign

Abstract : The 2D Wavelet-Transform Modulus Maxima (WTMM) method was used to detect microcalcifications (MC) in human breast tissue seen in mammograms and to characterize the fractal geometry of benign and malignant MC clusters. This was done in the context of a preliminary analysis of a small dataset, via a novel way to partition the wavelet-transform space-scale skeleton. For the first time, the estimated 3D fractal structure of a breast lesion was inferred by pairing the information from two separate 2D projected mammographic views of the same breast, i.e. the cranial-caudal (CC) and mediolateral-oblique (MLO) views. As a novelty, we define the “CC-MLO fractal dimension plot”, where a “fractal zone” and “Euclidean zones” (non-fractal) are defined. 118 images (59 cases, 25 malignant and 34 benign) obtained from a digital databank of mammograms with known radiologist diagnostics were analyzed to determine which cases would be plotted in the fractal zone and which cases would fall in the Euclidean zones. 92% of malignant breast lesions studied (23 out of 25 cases) were in the fractal zone while 88% of the benign lesions were in the Euclidean zones (30 out of 34 cases). Furthermore, a Bayesian statistical analysis shows that, with 95% credibility, the probability that fractal breast lesions are malignant is between 74% and 98%. Alternatively, with 95% credibility, the probability that Euclidean breast lesions are benign is between 76% and 96%. These results support the notion that the fractal structure of malignant tumors is more likely to be associated with an invasive behavior into the surrounding tissue compared to the less invasive, Euclidean structure of benign tumors. Finally, based on indirect 3D reconstructions from the 2D views, we conjecture that all breast tumors considered in this study, benign and malignant, fractal or Euclidean, restrict their growth to 2-dimensional manifolds within the breast tissue
Document type :
Journal articles
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-01557073
Contributor : Bernadette Bergeret Connect in order to contact the contributor
Submitted on : Friday, September 23, 2022 - 5:09:15 PM
Last modification on : Friday, September 23, 2022 - 5:15:54 PM

File

batch1.pdf
Publisher files allowed on an open archive

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

Collections

Citation

K. A. Batchelder, A. B. Tanenbaum, S. Albert, L. Guimond, P. Kestener, et al.. Wavelet-based 3D reconstruction of microcalcification clusters from two mammographic views: new evidence that fractal tumors are malignant and Euclidean tumors are benign. PLoS ONE, 2014, 9 (9), pp.e107580. ⟨10.1371/journal.pone.0107580⟩. ⟨hal-01557073⟩

Share

Metrics

Record views

90

Files downloads

0