Texture analysis by multi-resolution fractal descriptors

This work proposes a texture descriptor based on fractal theory. The method is based on the Bouligand-Minkowski descriptors. We decompose the original image recursively into 4 equal parts. In each recursion step, we estimate the average and the deviation of the Bouligand-Minkowski descriptors computed over each part. Thus, we extract entropy features from both average and deviation. The proposed descriptors are provided by the concatenation of such measures. The method is tested in a classification experiment under well known datasets, that is, Brodatz and Vistex. The results demonstrate that the proposed technique achieves better results than classical and state-of-the-art texture descriptors, such as Gabor-wavelets and co-occurrence matrix.Comment: 8 pages, 6 figure

Ray casting implicit fractal surfaces with reduced affine arithmetic

A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray. The method is also efficient due to a modification in the affine arithmetic representation that introduces a condensation step at the end of every non-affine operation. We show that our method is able to retain the tight estimation capabilities of affine arithmetic for ray casting implicit surfaces made from procedural noise functions while being faster to compute and more efficient to store

Texture analysis of aggressive and nonaggressive lung tumor CE CT images

This paper presents the potential for fractal analysis of time sequence contrast-enhanced (CE) computed tomography (CT) images to differentiate between aggressive and nonaggressive malignant lung tumors (i.e., high and low metabolic tumors). The aim is to enhance CT tumor staging prediction accuracy through identifying malignant aggressiveness of lung tumors. As branching of blood vessels can be considered a fractal process, the research examines vascularized tumor regions that exhibit strong fractal characteristics. The analysis is performed after injecting 15 patients with a contrast agent and transforming at least 11 time sequence CE CT images from each patient to the fractal dimension and determining corresponding lacunarity. The fractal texture features were averaged over the tumor region and quantitative classification showed up to 83.3% accuracy in distinction between advanced (aggressive) and early-stage (nonaggressive) malignant tumors. Also, it showed strong correlation with corresponding lung tumor stage and standardized tumor uptake value of fluoro deoxyglucose as determined by positron emission tomography. These results indicate that fractal analysis of time sequence CE CT images of malignant lung tumors could provide additional information about likely tumor aggression that could potentially impact on clinical management decisions in choosing the appropriate treatment procedure

Application of Fractal Dimension for Quantifying Noise Texture in Computed Tomography Images

Purpose Evaluation of noise texture information in CT images is important for assessing image quality. Noise texture is often quantified by the noise power spectrum (NPS), which requires numerous image realizations to estimate. This study evaluated fractal dimension for quantifying noise texture as a scalar metric that can potentially be estimated using one image realization. Methods The American College of Radiology CT accreditation phantom (ACR) was scanned on a clinical scanner (Discovery CT750, GE Healthcare) at 120 kV and 25 and 90 mAs. Images were reconstructed using filtered back projection (FBP/ASIR 0%) with varying reconstruction kernels: Soft, Standard, Detail, Chest, Lung, Bone, and Edge. For each kernel, images were also reconstructed using ASIR 50% and ASIR 100% iterative reconstruction (IR) methods. Fractal dimension was estimated using the differential box‐counting algorithm applied to images of the uniform section of ACR phantom. The two‐dimensional Noise Power Spectrum (NPS) and one‐dimensional‐radially averaged NPS were estimated using established techniques. By changing the radiation dose, the effect of noise magnitude on fractal dimension was evaluated. The Spearman correlation between the fractal dimension and the frequency of the NPS peak was calculated. The number of images required to reliably estimate fractal dimension was determined and compared to the number of images required to estimate the NPS‐peak frequency. The effect of Region of Interest (ROI) size on fractal dimension estimation was evaluated. Feasibility of estimating fractal dimension in an anthropomorphic phantom and clinical image was also investigated, with the resulting fractal dimension compared to that estimated within the uniform section of the ACR phantom. Results Fractal dimension was strongly correlated with the frequency of the peak of the radially averaged NPS curve, having a Spearman rank‐order coefficient of 0.98 (P‐value \u3c 0.01) for ASIR 0%. The mean fractal dimension at ASIR 0% was 2.49 (Soft), 2.51 (Standard), 2.52 (Detail), 2.57 (Chest), 2.61 (Lung), 2.66 (Bone), and 2.7 (Edge). A reduction in fractal dimension was observed with increasing ASIR levels for all investigated reconstruction kernels. Fractal dimension was found to be independent of noise magnitude. Fractal dimension was successfully estimated from four ROIs of size 64 × 64 pixels or one ROI of 128 × 128 pixels. Fractal dimension was found to be sensitive to non‐noise structures in the image, such as ring artifacts and anatomical structure. Fractal dimension estimated within a uniform region of an anthropomorphic phantom and clinical head image matched that estimated within the ACR phantom for filtered back projection reconstruction. Conclusions Fractal dimension correlated with the NPS‐peak frequency and was independent of noise magnitude, suggesting that the scalar metric of fractal dimension can be used to quantify the change in noise texture across reconstruction approaches. Results demonstrated that fractal dimension can be estimated from four, 64 × 64‐pixel ROIs or one 128 × 128 ROI within a head CT image, which may make it amenable for quantifying noise texture within clinical images