# Coherence Enhancement Based on Recursive Anisotropic Scale-Space with Adaptive Kernels
## 5 Experimental Results  
In this section, we provide quantitative and qualitative results for curvilinear structure detection using satellite images and lung CT images. Please note that the number of data used for the evaluation of the proposed algorithm is limited due to the short of availability in manual annotations given by medical experts such as radiologists. Our proposed recursive anisotropic diffusion algorithm constructs representations that improve the linear features and extract the curvilinear structures. We qualitatively and quantitively compared the algorithm against isotropic diffusion using a Gaussian kernel, anisotropic diffusion based on the scalar diffusivity function [25], and anisotropic diffusion based on the vector-valued diffusivity function with enhanced coherence features [44]. Some of the example data are presented in Figure 1, which shows (a) an aerial image as well as (b) sagittal plane, (c) axial plane, and (d) coronal plane lung volume CT images from left to right. To demonstrate the scale-space developed by the proposed recursive anisotropic diffusion process, a series of diffused images at varying scales are presented in Figure 2, where (a) the original image, and the diffused images at scales (b) \(t=10\), (c) \(t=30\), (d) \(t=50\), and (e) \(t=100\) are shown from left to right. The qualitative visual comparisons of the diffusion process for the aerial image and for the sagittal, axial, and coronal plane lung CT images are presented from top to bottom in Figure 3. In this figure, (a) shows the original image, and (b)-(e) display the diffused images obtained via the isotropic scheme using a Gaussian kernel, the anisotropic scheme proposed by [PERSON] [25], the coherence-enhancing scheme proposed by [PERSON] [44], and our proposed algorithm using recursive anisotropic diffusion, respectively, from left to right. As shown in the figures, a variety of linear features corresponding to roads and anatomical partitions are effectively characterized in the diffusion images obtained from our proposed algorithm. We apply a curvilinear detection algorithm based on the saliency measure on the characteristic representations with respect to linear features obtained via isotropic diffusion using a Gaussian kernel, anisotropic diffusion using a scalar diffusivity function, anisotropic diffusion using a vector-valued diffusivity function, and our recursive anisotropic diffusion algorithm. The detection of curvilinear features is visually presented in Figure 4, where the detection results are shown on the bottom row, the ground truth on the middle row, and the obtained diffused images on the top row. Figure 4 shows the diffusion images that were obtained via (a) isotropic diffusion, (b) the anisotropic diffusion method developed by [PERSON], (c) the coherence-enhancing method developed by [PERSON], and (d) our proposed diffusion algorithm, from left to right. The ground truth for the detection of fissures in lung CT images was obtained by the radiologist with manual annotations. For the detection of roads in the satellite images, the ground truth was obtained by human annotations based on the assumption that the central lines between relatively large blocks are likely to be roads. As shown in the detection results, our proposed algorithm has better accuracy and fewer false positives. Figure 1: Examples of images that were used for the experiment. The images under consideration have linear features that are of geometrical or anatomical significance. (**a**) Aerial image. (**b**) Lung CT (sagittal). (**c**) Lung CT (axial). (**d**) Lung CT (coronal). Figure 2: (**a**) the original aerial image and the resultant images obtained using the proposed method (i.e., recursive anisotropic diffusion) with the scales (**b**) \(t=10\), (**c**) \(t=30\), (**d**) \(t=50\), and (**e**) \(t=100\). The linear features corresponding to roads are better characterized as the anisotropic scale increases while the linear features are preserved.