# Coherence Enhancement Based on Recursive Anisotropic Scale-Space with Adaptive Kernels
## 5 Experimental Results
The results of fissure detection in the sagittal plane lung CT image are presented in Figure 5, where the diffused images are shown in the top row, the ground truth for the fissure to be detected is shown in the middle row, and the detection results for the fissure are shown in the bottom row. The diffused images shown in Figure 5 were obtained via (a) isotropic diffusion, (b) anisotropic diffusion method proposed by [PERSON], (c) coherence-enhancing diffusion method proposed by [PERSON], and (d) our proposed algorithm, from left to right. As shown in the detection results, our algorithm outperforms the other algorithms in terms of both accuracy and sensitivity. Figure 3: Qualitative comparison of image representations for (**a**) the original image and the diffused images obtained using diffusion processes based on (**b**) isotropic diffusion using a Gaussian kernel, (**c**) anisotropic diffusion via the method proposed by [PERSON] [25], (**d**) coherence-enhancing diffusion via the method proposed by [PERSON] [44], and (**e**) our proposed algorithm using recursive anisotropic diffusion. the diffusion results are shown for the aerial, lung CT (sagittal), lung CT (axial), and lung CT (coronal) images from top to bottom. The result of the detection of fissures in the coronal and axial plane lung CT images is visually presented in Figure 6, where the ground truths and detection results are shown together. The quantitative ROC analysis results for the detection of (a) roads in the aerial image and fissures in the (b) coronal, (c) axial, and (d) sagittal plane lung CT images in Figure 7 show that our algorithm outperforms the others. In the analysis of ROC curves, false positive indicates the detection of pixels that should not be categorized into any curvilinear feature and false negative indicates the miss of pixels that should be detected as curvilinear features. The precision and recall are computed for the detection of curvilinear features corresponding to roads in aerial images and fissures in coronal, axial, and sagittal plane CT images and presented in Table 1. Our algorithm consistently exhibits better results for both the precision and recall across different detection thresholds \(\theta\). The F-1 score is also computed for the detection of curvilinear features in Table 2 where the higher value indicate better performance. the accuracy was obtained based on the detection scheme that is determined by the overlap within a circular neighbourhood with respect to each location under determination. For each point \(x\in\Omega\), its associated circular neighbourhood is defined by \(B_{x}=\{y|\|x-y\|\leq 5\}\). Thus, the detection is determined as true when it has an overlap with respect to the circular neighbourhood of the reference. Figure 4: Examples of the detection results for the curvilinear structures in an aerial image using (**a**) isotropic diffusion, (**b**) anisotropic diffusion method proposed by [PERSON], (**c**) coherence-enhancing diffusion method proposed by [PERSON], and (**d**) recursive anisotropic diffusion using our proposed algorithm. Figure 5: Example of detection results for a curvilinear structure in the lung CT (saggital) image using (**a**) isotropic diffusion, (**b**) anisotropic diffusion proposed by [PERSON][PERSON], (**c**) coherence-enhancing diffusion proposed by [PERSON], and (**d**) recursive anisotropic diffusion via our proposed algorithm. Figure 6: Visual illustration of the fissure detection results in lung CT images. (**a**) Ground truth and (**b**) fissure detection for the coronal plane. (**c**) Ground truth and (**d**) fissure detection for the axial plane.