Multivariate data visualization using shadow

Transcription

1 Proceedings of the IIEEJ Ima and Visual Computing Wor Kuching, Malaysia, Novembe Multivariate data visualization using shadow Zhongxiang ZHENG Suguru SAITO Tokyo Institute of Technology ABSTRACT When visualizing data, one expected effect is to overview the data intuitively. In case of multivariate data visualization, combinations of visual cues which are color, texture, shape, size and orientation have been used. In this study, we focus on shadow which is distinguished from texture or color gradation unconsciously by human perception as a new visual cue for visualization, and introduce three methods which use shadows for multivariate data visualization. These are shadow by cylinder, texture-like shadow, and the combination of them. As the experimental result, we show visualization images that these methods make from weather data. 1 INTRODUCTION When visualizing data, one expected effect is to overview the data intuitively. Especially in case of visualizing multivariate data, it is very useful to display them at the same time. In that case, it is necessary to display the values so that viewer can read each element separately. Elements that have been used to visualize multivariate data are color, texture, shape, size and orientation. Visualization has been achieved by using these elements together[1]. In this study, we focus on the shadow which has not been used as an element for visualization. When considering the effect of the shadow, the presence of the shadow will become an important clue for the relationship of object positions, the shape of the shadow receiver s surface and the shape of the occluder[2]. In addition, we can cancel the change of color caused by the shadow as 1 we realize through some optical illusions[3]. That is, change of color by the base color change and by shadow can unconsciously be recognized separately. Therefore, We propose visualization methods that uses these characteristics of the shadow. 2 PREVIOUS WORK When using colors for multivariate data visualization, a certain color property tends to reduce readability of other properties. Rheingans showed that the difficulty of reading can be reduced by using multivariate data with the pair of hue and brightness is relatively lower than other pairs of color properties[4]. Several methods which use texture for visualization were proposed. Natural textures which are more intricate and rich in detail than standard primitives archives more vast and comprehensive data representation than standard primitives are used for multivariate data visualization[5]. To visualize multivariate data, data attributes correspond to the scale, orientation and brightness of textures respectively[6]. However, these correspondence is not intuitive to understand. In this paper, we propose the technique which is easy and intuitive to read the value like a bar graph. Colin[7] proposed the method to visualize two variables with high readability by using textures and colors together. However textures are overlapped on background colors, important information may be covered completely by these textures. We propose the visualization technique using the shadow which does not hide background colors completely.

2 3 OUR METHOD We introduce three methods which use shadows for multivariate data visualization. There are shadow by cylinder, texture-like shadow, and the combination of them. 3.1 Shadow by cylinder with bump shade The data to be displayed is 2 variate data which can be mapped on a plane. var 1 and var 2 take the values from 0 to 1. var 1 decides a color and var 2 corresponds to height. These two values generates a colored bump surface. Hereafter, the color determined by var 1 is called ground color. After performing the spline interpolation to var 2, a smooth bump surface whose height is decided by var 2 is generated. We display the local difference of the surface by shade. In order to distinguish the color changes by shade and by shadow, we use the technique based on the idea of the cold-to-warm tone[8] for shading. Shading is displayed using the tone of dark blue to bright yellow. Red to green tone is used for displaying var 1 as ground color. In order to display the absolute height at points on the surface, we put cylinders whose height and thickness are proportional to the height at the points. The heights of cylinders are displayed by casting shadows to surface. The form of a shadow is dependent on both the form of a surface which the shadow is cast on and the shape of an occluder. To get information from the length of shadows, the length of shadows should only be proportional to the height of cylinders. If the generated surface is the real bump surface, the length of shadows is not proportional to the height of cylinders under the influence of surface. To avoid this, the bump surface is expressed only by shading like bump mapping in our method. That is, the shadows which appear with cylinders are displayed as if on the flat plane. Cylinders are put randomly to avoid overlap of shadows. The actual calculation of RGB color C of a pixel is performed by the following equations with constants L, k, s, t, u, 2 C = LabtoRGB(l, a, b), (1) l = L + s shade t(1 shadow), (2) a = k(var 1 0.5), (3) b = u shade and (4) shade = l n, (5) where LabtoRGB(l, a, b) is the function which calculates RGB color from CIELAB color, shadow is the ratio of shadow, whose range is 0 to 1, and l and n are the normalized light vector and the normalized normal vector at the pixel calculated from fake bump surface. When pixel is in a shadow completely and shadow becomes 0 which is calculated by PCF[9]. 3.2 Texture-like shadow Considering with the possibility of the simultaneous use with shadow by cylinder we design one more type of shadow, texture-like shadow. To display shadow by cylinder with shading and texture-like shadow at the same time, we need to use marks which is easy to distinct and read values. We use a series of marks as shown in Fig. 1. A texture-like shadow is equal to an orthogonal projection of a occluder. Occluders whose shape varied by var 2 are set above the camera and a parallel light is put above the occluders. Size of occluders is varied so that the size of a shadow becomes the largest when var 2 = 1 and becomes smallest when var 2 = 0. Since it is guaranteed that these shadows do not overlap, these shadows can be expressed in higher density than shadows by cylinder. When displaying var 1 using color and var 2 with texture-like shadow simultaneously, equation (1), (2), and (3) are calculated with b = Combined method We consider the combination of color, shade, shadow by cylinder, and a texture-like shadow to visualize 3 variate data. When combining shadow by cylinder and a texture-like shadow, two light sources are required

3 s and t are related with the change of brightness. When s and u are large, the bumpy surface is easy to see. When t is large, shadows become dark and become easy to see. However the readability of ground color is reduced when s,u and t are too large. Figure 1: Example of texture-like shadow. Display values which change from 0 to 1 continuously. to generate two kinds of shadows. Because the densities of a shadows are different, the influence to the readability of ground colors are also difference. The distance of shadows in texture-like shadow is adjusted to be shorter than the average distance of cylinders. The darkness of texture-like shadow are adjusted to be brighter than shadow by cylinder by adjusting intensity of lights. When calculating a final color, the same calculation as Sec. 3.1 is performed under each light source condition, and the values of shade and shadow are decided by the weighted average with equations, shade = w 1shade 1 + w 2 shade 2 w 1 + w 2 and (6) shadow = w 1shadow 1 + w 2 shadow 2 w 1 + w 2 (7) where, w 1 and w 2 are the intensities of light sources and shade 1, shade 2, shadow 1 and shadow 2 are results of shade and shadow under each light source. 3.4 setting of parameters and a light sources Five coefficients L, k, s, t, u are used in these proposal techniques. L is the coefficient of the brightness of ground color, s is the coefficient of change on color axis of green to red, s is the coefficient of brightness change by shading, t is the coefficient of the decrease of brightness by a shadow and u is the coefficient of change on color axis of blue to yellow which caused by shading. Readability depends on these five coefficients. Since ground colors become dark by a shadow, L should take a large value. When k is larger, the ground color becomes more vivid. However the color will be out of the RGB color space if k is too large. Both 4 RESULTS We show results of our method applied for weather data. We set parameters as L = 70, k = 70, s = 20, t = 15, u = 20 in Fig.2(a)(b) and L = 70, k = 70, s = 20, t = 35, u = 20 in Fig.2(c). In these results, color, shade and shadow by cylinder and texture-like shadow correspond to temperature, wind speed and humidity respectively. Fig.2(a) shows temperature and wind speed. Fig.2(b) shows temperature and humidity. Fig.2(c) shows temperature, wind speed and humidity. In each case, the color element under shadows is easy to see. By combining shadow by cylinder and shade for one variate, we can see both local differences with high resolution and absolute values. Shadow by cylinder and texture-like shadow are easy to distinguish, even they are overlapped. The shade of a bump surface and the length of shadows by cylinder, visualize local change and absolute value of data respectively. Showing change of colors by shadow and shade with different color axis, we can read two types of color changes separately. Fig.3 are results of every 6 hours of weather data. We can recognize that the big wind region moves from south of Japan to middle of Japan easily. 5 CONCLUSION We proposed three visualization methods to visualize multivariate data using shadows, shade and ground color. In our methods, shadows do not hide ground colors completely and we can read both shadows and ground colors easily. To distinguish shade and shadows, these change of color is rendered with different color axes. As future work, we will perform user tests to evaluate out methods. 3

4 (a)result using color, shade and shadow by cylinder (b)result using color and texture-like shadow (c)result using color, shade, shadow by cylinder and texture-like shadow Figure 2: Example results by three methods. 4

5 Figure 3: Results which visualize weather data of every 6 hours. 5

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