# Haptic Texture Rendering of 2D Image Based on Adaptive Fractional Differential Method
## 7 Experiment  
The experimental system for haptic texture rendering of 2D images consists of a Phantom Omini haptic device and a computer, shown in Figure 5. The Phantom Omini  
Figure 4: Two-dimensional texture tangential force vectors of grey image. (**a**) texture feature extracted from “Lena” image using fractional differential method (v = 0.55); (**b**) texture tangential force vectors in amplified red square area in (**a**).  
haptic device has a six degrees of freedom position/attitude detection and a three degrees of freedom force feedback with the maximum force of 3.3 N. Its workspace is 160 mm width \(\times\) 120 mm height \(\times\) 70 mm depth with location accuracy 0.055 mm.  
In this experimental system, we selected five images with 500 \(\times\) 500 pixels from the Brodatz texture image database [41] and used the proposed adaptive fractional differential method to extract the texture features, shown in Table 2. Then, we used the proposed haptic texture rendering model to render the object surface based on the extracted texture. In order to verify the effect of our method, 20 volunteer subjects (10 male and 10 female, aged 21 to 31) is randomly selected to perform the texture perception experiments. The subject just haptically felt the surface of 25 2D images, which are stochastically produced by a computer one by one, and classified them into 5 types of images by using the Phantom Omini haptic device without any visual information of the 2D image.  
The appearance of the original image and the texture image are hidden, and only the calculated texture force is mapped to a smooth virtual plane of 500 \(\times\) 500 pixels. The calculation of the constraint force of the virtual plane is based on [PERSON]'s law. When the volunteers \"groped\" the \"blank\" virtual plane, the hand controller fed back the texture force of the image together with the constraint force of the virtual plane to the subject. Volunteers need to select the image to be reproduced by force/haptic sense of texture from five original images according to the perceived texture, and then count the correct rate of volunteers' perception of each image.  
The experimental results show that the average classification accuracy of 5 types of images based on haptic feelings are 87%, 72%, 81%, 91%, and 83%, shown in Figure 6. It is obvious that the proposed haptic texture rendering method can help users understand the texture contents of the image. So, it is an effective approach of image-based haptic texture rendering.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Image 1** & **Image 2** & **Image 3** & **Image 4** & **Image 5** \\ Original images & & & & & \\ \hline Extracted textures & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Texture feature extracting of 2D images using adaptive fractional differential method.  
Figure 5: The experimental system of haptic texture rendering of 2D image.  
Further, we conducted another group of experiments, we selected four 2D images, and extracted their texture features through the proposed adaptive algorithm, shown in Table 2. It can be seen from the extraction results that the image texture extracted by the adaptive fractional differentiation algorithm is clear and the details are retained completely, which indicate the excellent effect of the adaptive fractional differentiation algorithm in extracting the detail texture.  
The TV-Gabor model is used for comparison (the TV-Gabor model decomposes the image by using the prior conditions of frequency and texture direction, so as to distinguish the contour shape of the image body from the texture part), and selected 4 real object images with textures, shown in Table 3. Similarly, we used the proposed Haptic texture rendering model to render the object surface based on the extracted texture. In the cases where the volunteers were blindfolded, we calculated the correct rate of each image recognition, shown in Figure 7. It is verified again that the texture feature outputs by the tactile texture rendering