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indicated that there is no difference in sensitivity to vertical and horizontal movement, but that judgmental-standards asymmetries exist. Soeta et al. (2003) showed that subjective preference for vertical movement was more sensitive than that for horizontal movement; that is, asymmetry in the sensitivity. Thus, more attention to sensitivity is needed for the vertical direction because of the sharp decline of subjective preference in the fast-moving range.
14.3 Subjective Preferences for Texture
Evaluation of subjective preference of texture was conducted by the PCT. By averaging the scale values of all subjects, it was found that the most preferred value of φ1 for texture regularity extracted from the spatial ACF is approximately given by [φ 1]p ≈ 0.41. As an application, a suggestion is offered here that artistic expressions of color modulation and sequential form be realized in a drawing.
14.3.1 Preferred Regularity of Texture
In a manner similar to that described in Section 14.2, the four factors were extracted from the two-dimensional ACF (Fujii and Ando, unpublished data). To compare the degree of periodicity, the amplitude of the first peak in the ACF, φ1, was considered under the condition of a roughly constant δ1. As a first approximation in the previous section, rating of the φ1 value could represent perceived regularity of texture (Equation (13.5)). If the size and shape of the materials and the spacing between the objects in the pattern are completely equal, the calculated ACF does not decay. This means that such a texture is, theoretically, perfectly regular. However, if the materials contain a kind of fluctuation of the object size and spacing and nonuniformity of the light reflection, then the ACF gradually decays, and the value of φ1, which is a measure of perceived regularity, is considered as the measure for the degree of fluctuation in texture.
Ten 22to 24-year-old subjects participated in the experiment. All had normal or corrected-to-normal visual acuity. Stimuli were presented on a display under a dark surrounding. The display was set at a distance of 1.5 m from the subjects. Subjects were presented pairs of two stimuli and asked to judge which they preferred (PCT). All possible pairs from the five selected stimuli as shown in Fig. 14.9 were presented in a random order in one session. All subjects conducted 10 series of sessions, giving a total of 100 judgments.
Results for all subjects are shown in Fig. 14.10. The scale value of the subjective preference has a single peak value for each subject, even allowing some individual differences. The most preferred range was found in the value of φ1 for each subject. Subjects did not prefer textures that had a too high or too low a value of φ1. By averaging the scale values of all subjects, it was found that [φ1]p ≈ 0.41 was the most preferred value for texture regularity. The coefficients in Equation (14.1) with the number of subjects was α ≈ 3.9 and β = 3/2.
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Fig. 14.9 Two-dimensional spatial textures used with the value of φ1 for the subjective preference judgment
Fig. 14.10 (a) Scale values of preference for individual subjects. (b) Averaged values. For averaged values, a fitting curve with the 3/2 power of φ1 in Equation (14.1) is shown
It is worth noting that the most preferred subjective preference of the flickering light with fluctuation as described in Section 14.1 is [φ1]p ≈ 0.46 as well. It is considered, therefore, that a certain degree of fluctuation in both temporal and spatial factors is a visual property affecting subjective preference.
14.3.2 Application: Spatial “Vibrato” in a Drawing
Artistic expressions may be found in Photo 14.1, which was personally provided by Werner Lauterborn in 2003 and photographed by Gisa Kirschmann Schroeder at
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Photo 14.1 An inspiration from the cave paintings in the cave "Cosquer" near Marseille, France (Lauterborn, 2003)
the Third Physics Institute, University of Goettingen. This painting was composed and interpreted by Lauterborn based on an inspiration from cave paintings dated approximately 18,500 years ago that were discovered in the cave "Cosquer" near Marseille, France, which is accessible only via an underwater entrance by diving (Clottes and Courtin, 1995).
It is interesting to point out the fact that color modulation, expressed by Lauterborn as a form of “vibrato,” is present in the background being a kind of cave wall. Also, the horsehair sequence of a “vibrato” in the spatial frequency might be analyzed by the ACF of images with the gray level. There is a certain degree of similarity as mentioned above, which is discussed both in the time domain analysis of the flickering light and in the spatial domain relating to subjective preference, respectively. The horsehair sequence is periodic, not perfect or just random, and there is a certain degree of fluctuation like vibrato. In fact, the factor φ1 extracted from the ACF is around 0.3, which is a range of the most preferred condition depending on the individual (Fig. 14.10). Regarding such color modulation including the effect of gray level, further attempts could be made to investigate the physical factors with multiple-dimensional correlation analysis. Lauterborn said that Photo 14.1 was painted in the years between 2001 and 2003. As a matter of fact, ideas of such a color modulation and a vibrato in the periodic structure came out without his conscious process. He could not identify how he painted it, because such kinds of ideas of beauty come from “out of time” or “beyond any specified time.” Therefore, this process may relate to the “third stage of time” (Ando, 2004).