Our brain tends to associate a certain feature in one sensory modality with a feature in another modality in a non-random manner, which is known as “cross-modal correspondence” (Marks, 2004; Spence, 2011). For example, auditory pitch is known to be associated with visual luminance (Wicker, 1968; Marks, 1974), shape (Marks, 1987; Walker et al., 2010), and size (Gallace and Spence, 2006; Parise and Spence, 2009; Evans and Treisman, 2010; Bien et al., 2012). In addition, tactile properties such as vibrotactile frequency/amplitude and haptic properties such as smoothness, softness, and roundness are systematically related to visual features such as lightness and color (Martino and Marks, 2000; Ludwig and Simner, 2013; Slobodenyuk et al., 2015; Delazio et al., 2017). Such correspondence between perceptual features occurs not only across sensory modalities but also within a single modality. In recent years, there has been a growing interest in this intra-modal correspondence, especially within the visual modality between numerous visual properties (size, direction, amount, intensity; Lindauer, 1969) or graphemes (Simner et al., 2005; Lau et al., 2011) and color. One of the most representative types of intra-modal correspondence is shape-color correspondence.

A classic shape-color correspondence was first suggested by Kandinsky in the early 20th century. He proposed a fundamental association between primary shapes and colors (triangle with yellow, square with red, and circle with blue) based on the survey he conducted (Droste, 1990; Lupton and Miller, 1991; Gage, 1993). However, subsequent surveys attempting to replicate Kandinsky’s results did not converge (Jacobsen, 2002; Jacobsen and Wolsdorff, 2007; Kharkhurin, 2012). Also, studies utilizing the Implicit Association Task (IAT) failed to verify the associations postulated between Kandinsky’s three shapes and colors though they hypothesized that participants would show faster RTs when the response key mapping matched the proposed associations (Makin and Wuerger, 2013; Chen et al., 2015b).

Previous studies have mainly utilized discrete primary geometric shapes (i.e., circle, triangle, square, and hexagon) and colors (i.e., red, yellow, and blue) in a one-to-one matching task (Makin and Wuerger, 2013; Chen et al., 2015b,2016). However, such cases have not considered that shapes have multiple properties such as complexity, pointedness, symmetry, and regularity, each of which is influential of the outcome shape (Pizlo, 2010). Among a few studies of shape-color correspondence that have acknowledged this, shape complexity has been a topic of interest (Malfatti, 2014; Chen et al., 2016; Dreksler and Spence, 2019). Several studies manipulated shape complexity into multiple levels (Malfatti, 2014; Dreksler and Spence, 2019). Specifically, in Malfatti (2014), shape complexity was considered by the number of points into three levels but was not found to be associated with color (luminance and saturation). In a subsequent study by Dreksler and Spence (2019), the extent of shape complexity was changed into three or four levels with respect to the number of sides or levels of concavities. However, inconsistent results were found in the different experiments of the study: complex shape showed a relationship with both dark (Experiments 1 and 2) and light colors (Experiment 3).

Next, color is composed of three elements: hue, luminance, and saturation. In contrast to most previous studies which only included hue in the discourse of shape-color correspondence, recent research began considering all three elements when investigating whether a specific shape is associated with a specific color. For example, in the study of Dreksler and Spence (2019), ten hues were chosen and presented at two different levels of luminance (light and dark) and at full saturation. Malfatti (2014) employed a color set consisting of eight hues, provided at two levels of luminance (light and dark) and saturation (saturated and muted). However, the results of the relationship between shape complexity and luminance/saturation of these two studies were inconsistent; a close association between complexity and luminance was shown in one study (Dreksler and Spence, 2019), whereas complexity was not associated with luminance and saturation in the other (Malfatti, 2014). Commonly, both studies divided luminance and saturation into two levels, though luminance and saturation vary continuously along each dimension. In the present study, to account for the continuity of shape and color features, we parametrically manipulated levels of shape and color. Specifically, we generated shapes whose complexity was manipulated in three levels, and colors in which their three elements (hue, luminance, and saturation) were shown on a continuous scale. By using these stimuli, we expected to gain a deeper understanding of shape-color correspondence.

A notable addition of the current study is the realistic 3D objects used as stimuli. Previous imaging studies have suggested overlapping activations in the brain during visual and haptic processing of 3D objects (Amedi et al., 2001; Kim and James, 2010). That there is a transfer of object shape information between vision and haptics was also supported by behavioral results (Gibson, 1963; Newell et al., 2001; Norman et al., 2004). Taken together, shape properties are extracted from objects not only by visual exploration but also haptic exploration of those objects, and exploring objects in both visual and haptic modalities would provide a more comprehensive percept of 3D shapes. By using 3D shape stimuli and exploring the object both visually and haptically, we expected the added haptic modality to facilitate the effects of visual shape-color correspondence.

With two experiments, the current study aimed to closely examine the patterns of correspondence between shape complexity and color in terms of hue (Experiment 1), luminance, and saturation (Experiment 2). In Experiments 1 and 2, participants were presented with the 3D shapes – in either visual (video clips of 3D objects) or visuo-haptic (viewing 3D-printed objects while exploring it with their hands) modes of exploration. Subsequently, they had to pick from a color palette the color best matching each shape of the object. To examine the systematic patterns of correspondence between shape complexity and color, we parametrically manipulated the levels of both shape and color stimuli. The shapes of 3D objects were manipulated into three levels of complexity. For the color stimuli, hue was presented at eight levels (Experiment 1) and both luminance and saturation were divided into fifteen levels (Experiment 2). In addition, utilizing 3D shapes allowed us to test the modulatory effect of exploration modality. Reflecting the way our stimuli were manipulated, we hypothesized that shape complexity is systematically related to color including hue, luminance, and saturation. We also hypothesized that the non-arbitrary mapping between shape complexity and color is modulated by the modality of exploration (i.e., visual or visuo-haptic).

The present study demonstrates a non-arbitrary association between shape and color. Importantly, using parametrically manipulated 3D shape and color stimuli enabled us to more closely examine the shape-color correspondence. The associated colors showed systematic modulations according to the complexity of 3D shapes. Specifically, results of Experiment 1 showed that as shapes became more complex, the best associated hue changed from those with long wavelengths to ones with short wavelengths. In Experiment 2, we found that with increasing shape complexity, the associated luminance decreased and the associated saturation increased. Moreover, when haptic exploration was combined with visual exploration, there was an added effect to the association between shape complexity and elements of color–for saturation in particular. The results imply a non-random mapping between shape complexity and color including hue, luminance, and saturation. It also suggests the importance of considering haptic characteristics of shape when examining shape-color correspondence.

Our results of Experiment 1 are in line with those from previous studies to show associations between 2D shape complexity and hues. Although results from three experiments of Dreksler and Spence (2019) were not consistent, their second experiment manipulating complexity into four levels demonstrated that shape with low-medium complexity was associated with yellow (Dreksler and Spence, 2019). Chen et al. (2016) examining cross-preference of shapes and colors showed that people who preferred simple shapes tend to prefer yellowish colors while people who preferred complex shapes tend to prefer bluish colors. Additionally, early studies examining shape-color correspondence with primary geometric shapes (i.e., circle, triangle, square, and hexagon) and colors (i.e., red, yellow, and blue) implied that shapes with more angles, namely complex shapes, are associated with hues with short wavelengths (Jacobsen and Wolsdorff, 2007; Albertazzi et al., 2013; Chen et al., 2015a,2016).

Our study is distinguished from previous studies by investigating luminance and saturation on a continuum. For instance, Dreksler and Spence (2019) manipulated luminance into two levels and showed conflicting results: associations between complex shape and dark color, and associations between complex shape and light color. In the study of Malfatti (2014), luminance and saturation were manipulated into two levels, respectively. However, the relationship between shape complexity and luminance/saturation was not found. It is probable that existing associations between shape and colors were not revealed because previous studies merely manipulated the stimuli in a binary manner. Dividing the wide spectrum of both luminance and saturation into multiple levels enabled us to examine the relationship between shape complexity and color in a more systematic manner. Therefore, we could find compelling evidence for a non-random mapping between shape complexity and luminance/saturation.

We used 3D modeling to create objects that enable dynamic haptic exploration, which proved to have several advantages. In our everyday lives, we encounter and interact with 3D objects. Among these interactive experiences, shape perception is a multisensory experience not only of vision but also including haptics. This has been evidenced by both behavioral and neuroscientific studies (Gibson, 1963; Amedi et al., 2001; Newell et al., 2001; Ernst and Banks, 2002; Norman et al., 2004; Kim and James, 2010). It is plausible that this multimodal characteristic of shape perception influences shape-color correspondence. Unlike previous studies that have only utilized 2D shapes, we used 3D shape stimuli which can be explored by both visual and haptic modalities to account for the multimodal nature of shapes when examining shape-color correspondence.

Using the 3D stimuli, our results displayed tighter patterns of associations in the multimodal exploration condition. Specifically, the association observed in the visual-only condition was significantly strengthened in the visuo-haptic condition for saturation while showing a tendency to do so for luminance. The results of visuo-haptic exploration are displaying a similar pattern of results with visual exploration can be attributed to the fact that vision and haptics share common brain regions such as the middle occipital (MO) cortex (James et al., 2002), the lateral occipital (LO) cortex (Malach et al., 1995; Grill-Spector et al., 2001), the lateral occipital tactile-visual (LOtv) (Amedi et al., 2001, 2002) and the intraparietal sulcus (IPS) (Culham and Kanwisher, 2001; Grefkes et al., 2002; Zhang et al., 2004; Stilla and Sathian, 2008). These results can also be understood in relation to the origin of cross-modal correspondence. One explanation for cross-modal correspondence is the long-term learning that reflects the statistical landscapes of everyday experience (Parise, 2016). As mentioned earlier, perception in our daily lives is more often multisensory than unisensory. Thus, tighter shape-color associations portrayed in the visuo-haptic exploration condition–which is closer to experience in everyday life–supports the statistical explanations of cross-modal correspondence.

The current study revealed that perceptual inputs from a single modality or different sensory modalities are closely associated with each other in a systematic and non-random manner. Yielding results that serve as significant empirical evidence for intra-modal/cross-modal correspondence between shape and color, the present study entailed several methodological advantages. First, parametrically manipulating the level of shape complexity and color and presenting the wide spectrum of both luminance and saturation allowed us to systematically examine the shape-color correspondence. Second, utilizing 3D shapes enabled us to consider the multimodal nature of shapes when examining shape-color correspondence. Our results have an important implication in the sense that it has potential for application in the industrial field. There have been attempts to apply the knowledge of cross-modal correspondence to branding and marketing (Klink, 2003; Lowrey and Shrum, 2007). In a similar vein, the current results could be a useful source for a design reflecting our innate associations between intra-modal/cross-modal features. Taken together, the present study provides a basic understanding of systematic shape-color correspondences with a possibility for application.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving human participants were reviewed and approved by the Korea University Institutional Review Board. The patients/participants provided their written informed consent to participate in this study.

JS, HS, MP, SN, and C-YK designed the experiment, analyzed the results, and revised the manuscript. JS, HS, MP, and SN conducted the experiment. JS, HS, MP, and C-YK drafted the manuscript. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.