Tone-based Shading of Matte Objects

  In a colored medium such as air-brush and pen, artists often use both hue and luminance (greyscale intensity) shifts. Adding blacks and whites to a given color results in what artists call shades in the case of black, and tints in the case of white. When color scales are created by adding grey to a certain color they are called tones  [2]. Such tones vary in hue but do not typically vary much in luminance. When the complement of a color is used to create a color scale, they are also called tones. Tones are considered a crucial concept to illustrators, and are especially useful when the illustrator is restricted to a small luminance range [12]. Another quality of color used by artists is the temperature of the color. The temperature of a color is defined as being warm (red, orange, and yellow), cool (blue, violet, and green), or temperate (red-violets and yellow-greens). The depth cue comes from the perception that cool colors recede while warm colors advance. In addition, object colors change temperature in sunlit scenes because cool skylight and warm sunlight vary in relative contribution across the surface, so there may be ecological reasons to expect humans to be sensitive to color temperature variation. Not only is the temperature of a hue dependent upon the hue itself, but this advancing and receding relationship is effected by proximity [4]. We will use these techniques and their psychophysical relationship as the basis for our model.

  

Figure 2: How the tone is created for a pure red object by summing a blue-to-yellow and a dark-red-to-red tone.

We can generalize the classic computer graphics shading model to experiment with tones by using the cosine term ($\mbox{${\bf \hat{l}}$} \cdot \mbox{${\bf \hat{n}}$}$) of Equation 1 to blend between two RGB colors, k_cool and k_warm:  

$$I = \left(\frac{1 + \mbox{${\bf \hat{l}}$} \cdot \mbox{${\bf... ...f \hat{l}}$} \cdot \mbox{${\bf \hat{n}}$}}{2} \right) k_{warm}$$ (2)

Note that the quantity $\mbox{${\bf \hat{l}}$} \cdot \mbox{${\bf \hat{n}}$}$ varies over the interval [-1,1]. To ensure the image shows this full variation, the light vector $\mbox{${\bf \hat{l}}$}$ should be perpendicular to the gaze direction. Because the human vision system assumes illumination comes from above [9], we chose to position the light up and to the right and to keep this position constant.

An image that uses a color scale with little luminance variation is shown in Figure 6. This image shows that a sense of depth can be communicated at least partially by a hue shift. However, the lack of a strong cool to warm hue shift and the lack of a luminance shift makes the shape information subtle. We speculate that the unnatural colors are also problematic.

In order to automate this hue shift technique and to add some luminance variation to our use of tones, we can examine two extreme possibilities for color scale generation: blue to yellow tones and scaled object-color shades. Our final model is a linear combination of these techniques. Blue and yellow tones are chosen to insure a cool to warm color transition regardless of the diffuse color of the object.

The blue-to-yellow tones range from a fully saturated blue: k _blue = (0, 0, b), b in the range [0,1], in RGB space to a fully saturated yellow:k _yellow = (y, y, 0), y in the range [0,1]. This produces a very sculpted but unnatural image, and is independent of the object's diffuse reflectance k_d. The extreme tone related to k_d is a variation of diffuse shading where k_cool is pure black and k_warm = k_d. This would look much like traditional diffuse shading, but the entire object would vary in luminance, including where $\mbox{${\bf \hat{l}}$} \cdot \mbox{${\bf \hat{n}}$} < 0$ is less than 0. What we would really like is a compromise between these strategies. These transitions will result in a combination of tone scaled object-color and a cool-to-warm undertone, an effect which artists achieve by combining pigments. We can simulate undertones by a linear blend between the blue/yellow and black/object-color tones:

Plugging these values into Equation 2 leaves us with four free parameters: b, y, $\alpha$, and $\beta$. The values for b and y will determine the strength of the overall temperature shift, and the values of $\alpha$, and $\beta$ will determine the prominence of the object color and the strength of the luminance shift. Because we want to stay away from shading which will visually interfere with black and white, we should supply intermediate values for these constants. An example of a resulting tone for a pure red object is shown in Figure 2.

Substituting the values for k_cool and k_warm from Equation 3 into the tone Equation 2 results in shading with values within the middle luminance range as desired. Figure 7 is shown with b = 0.4, y = 0.4, $\alpha$ = 0.2, and $\beta$ = 0.6. To show that the exact values are not crucial to appropriate appearance, the same model is shown in Figure 8 with b= 0.55, y = 0.3, $\alpha$ = 0.25, and $\beta$ = 0.5. Unlike Figure 5, subtleties of shape in the claws are visible in Figures 7 and  8.

The model is appropriate for a range of object colors. Both traditional shading and the new tone-based shading are applied to a set of spheres in Figure 9. Note that with the new shading method objects retain their ``color name'' so colors can still be used to differentiate objects like countries on a political map, but the intensities used do not interfere with the clear perception of black edge lines and white highlights.