Sunshine around the middle Earth: relief inversion less prevalent in satellite images in the near-south of the Equator than on the Equator

ABSTRACT

Inverted depth perception in satellite images is a well-known phenomenon. It has been previously verified that the illusion is prevalent in Northern Hemisphere (NH) images, while it is observed in Southern Hemisphere (SH) images to a much smaller extent. However, the equatorial zone has not been examined despite its interesting geometric position in relation to the Sun and satellite orbits. We present a user study (n = 313) in which participants were asked to identify landforms on 16 satellite images from the equatorial region. Our main findings are: (a) surprisingly, on the equatorial line and roughly ±1° of it in either direction, the results are consistent with the NH images; (b) instead, the expected variation/ambiguity occurs with the images 2–5° south of the Equator. These outcomes imply that based on illumination alone, the ‘middle’ (i.e. the Equator) might be somewhat more south from the perspective of the studied illusion. The observed effect surpasses various individual and group differences such as biological sex, expertise and education levels. Landcover cues such as snow, vegetation etc. do not appear to moderate the observed effect either. Our observations contribute towards a better understanding of the causes and prevalence of the relief inversion illusion.

KEYWORDS:

• Optical illusion
• pseudo-relief
• relief inversion
• terrain reversal
• reverse relief
• false topographic perception phenomenon

1. Introduction

The relief inversion effect is a perceptual illusion that most likely occurs as a result of an unconscious bias in human cognitive processing of visual information (Bravo 2014). With the relief illusion, a reversal of 3D shapes occurs in various media if shading and shadows are the main depth cues (Figure 1). The relief inversion phenomenon, or pseudo-relief, can occur in terrestrial images or abstract shapes (Figure 1), as well as in geospatial media (Figure 2) such as shaded relief maps (SRM) (Biland and Çöltekin 2017) or aerial/satellite images (Bernabé-Poveda and Çöltekin 2015). In geospatial sciences, the phenomenon is known by different names: relief inversion, terrain inversion, terrain reversal effect, topographic effect, pseudoscopic effect, pseudo-relief, and false topographic perception phenomenon (FTPP). In this manuscript, we use the term ‘relief inversion’, following Imhof’s (1965) 2007) terminology.

Figure 1. Left: Relief inversion in cuneiform writing showing a Sumerian sales contract. (a) Original view and (a’) 180°-rotated view resulting in reversed forms for majority of the viewers, e.g. turning concave borders of the rectangles in original view into convex lines in a’. Right: (b) digitally rendered abstract shape, (b’) 180°-rotated view with reversed forms. e.g. convex central area in b turns into concave form in b’ for majority of viewers. Source: (a) Public domain (Wikimedia Commons 2009), (b) Redrawn from Liu and Todd (2004).

Figure 2. Left: A NH region where the sun shines from the south, mapped with illumination from the south. For the majority of the viewers, the terrain is reversed or ambiguous in this case. Right: Same area with illumination from the north, which is correctly perceived by the majority of viewers. Sources: Relief Shading Website (2017) http://www.reliefshading.com/design/light-direction/ CC-BY.

The effect has been known in cartography for decades, and cartographers have addressed it when manually drawing cartographic relief in shaded relief maps (SRMs) by following the guidelines for its attenuation (Rittenhouse 1786; Imhof (1965) 2007). The same guidelines continue to be used in digital shading. These guidelines propose that the light source should be located with respect to the observer at an azimuth of 315° and an angle of incidence of 45° (Imhof (1965) 2007; Slocum et al. 2022; Kraak and Ormeling 2020). In recent years, a controlled experiment has demonstrated that the ideal illumination position may be closer to the north than the conventional 315° at 337.5° (Biland and Çöltekin 2017). Figure 3 illustrates the relief inversion effect in satellite images by showing them side-by-side with their 180°-rotated versions.

Figure 3. Images with the relief inversion effect (a, b, c) are the original images published by Google Maps. Rotating the images 180° restores the true relief (a’, b’, c’). (a) ABC is perceived as a ridge, even though it is a river. (b) and (c): Despite seemingly obvious clues, many people view houses as courtyards and streets as walls. Source: Own elaboration from Google Maps (Map data: ⓒ 2016 Google, Landsat).

In satellite images, the sun’s position in relation to the sun-synchronous image collection routines of satellite missions leads to relief inversion on a large part of the Earth's surface (Figure 4).

Figure 4. In the NH, the light comes from the south, leaving the northern slopes in shade, whereas in the SH light source is at the north. Source: (a) self-made. (b) redrawn from Bernabé-Poveda, Sánchez-Ortega, and Çöltekin 2011.

Due to the inclination of the Earth's axis with respect to the plane of the ecliptic through which the sun runs (Figure 4(a)), the lands located south of the Tropic of Capricorn will always be illuminated by the sun from the north (Figure 4(b)) and the lands located north of the Tropic of Cancer, they will always be illuminated from the south. The same problems occur in the intertropical zones, in which the sun is at some dates to the north and at others to the south (Figure 5).

Figure 5. The sun shines from the north in one season and from the south in another only in the intertropical areas. (a) On these dates, an object will have a near-zero shadow at the indicated locations. The two latitudes are in the tropics, corresponding to the highest and lowest values of solar declination. (b) Solar declination is 23.45° during the summer solstice (maximum), −23.45° during the winter solstice (minimum), and zero during the equinoxes. The sun is in the south from 21st Sept to 21st Mar, which is when relief inversion occurs in satellite (and aerial) images. (c) People (including two of the co-authors), and their shadows at noon on 23 Sept, 2014, in Sangolquí, Ecuador (0°20´S). Source: Authors’ elaboration.

During the 09:00 am to 11:00 am time window where sun-synchronous satellite images are acquired (Gil et al. 2014), the annual variation of shadows in the equatorial strip is high (with a shadow factor between 0.23 and 1.23), so this variation should be studied when evaluating relief perception. Given that satellite images are extensively used in multiple contexts, it is important to understand the implications of relief inversion illusion. Viewers are often unaware of relief inversion. In fact, the stronger the illusion, the more confident people feel in their ability to correctly identify landforms in an image that contains relief inversion (Çöltekin and Biland 2019), which can lead to potential confusion and errors. It has been demonstrated that the illusion is experienced by the majority of viewers, that is, with SRMs, this number can be as high as 98% when the light source is in the bottom left (Çöltekin and Biland 2019), and with satellite images, about 60% of the NH images where illumination predominantly comes from the bottom left (southwest) and northern slopes are shaded (Bernabé-Poveda and Çöltekin 2015). The relief inversion effect is also observed in SH images, although to a lesser extent, for example, Bernabé-Poveda and Çöltekin (2015) observed this to be approximately 25%. The prevalence of relief inversion is different for the satellite images and SRMs, seemingly because the photo-textures allow for additional interpretation (Çöltekin and Biland 2019), and it is different for NH and SH owing to the illumination angle, as explained above. The prevalence of the relief inversion effect has not been quantified with satellite images of equatorial areas, where the phenomenon, due to the variation of solar declination, changes throughout the year. In this study, we fill this gap by focusing on the equatorial region and documenting the relief inversion effect through a set of quantitative surveys with 313 participants. Below, we first provide a literature review and then detail our experiments and findings.

2. Background and related work

The relief inversion effect is similar to other alterations of perception, such as optical (e.g. Coren and Girgus 2022), acoustic (e.g. Biocca, Kim, and Choi 2001), olfactory (Stevenson 2011), gustatory (Narumi et al. 2011) and haptic illusions (Gentaz and Hatwell 2008; Norman et al. 2004). As such, the relief inversion phenomenon has been treated by several authors from different disciplines with varying goals. According to Liu and Todd (2004), this was first observed (at least documented) by German chemist and botanist Gmelin in 1744 (Brewster 1826). The oldest and most widely accepted explanation for the relief inversion phenomenon is attributed to Rittenhouse (1786) who argues that the brain is ‘used to’ processing images illuminated from above.

When light comes from below, or otherwise ambiguous shading is present in the scene, human perceptual-cognitive systems make assumptions about the objects as if they are illuminated from above (Rittenhouse 1786; Brewster 1826, 103). This assumption has been a dominant paradigm over time (Hindle and Hindle 1959; Berbaum, Bever, and Chung 1984; Adams 2007; Metzger and Spillmann 2006), and is well established across domains, including cartography for the shading of SRMs (Imhof (1965) 2007). This phenomenon is termed overhead illumination bias or light from above prior (Kleffner and Ramachandran 1992).

It has also been documented that there is a left bias (Mamassian and Goutcher 2001), that is, our perception of shapes from shading is most accurate when the light is above and above the left. Similarly, the shape-from-shading (SFS) model (Berbaum, Bever, and Chung 1984; Ramachandran 1988) posits that the presence or absence of shadows modifies the perception and understanding of relief. It has also been speculated that relief inversion is linked to various other phenomena. For example, the fact that gravity keeps most objects on the ground and thus the human brain is conditioned to see objects rather than above (Koenderink and van Doorn 1980), makes the lighting from below particularly difficult to interpret. Possibly as a moderating factor for relief inversion, global convexity bias (Liu and Todd 2004) is also often mentioned, which suggests that humans are more often used to seeing convex objects than concave objects.

There are also other signals or cues related to light, which are not related to the light-from-above hypothesis, called lighting cues, which can affect relief perception (Morgenstern, Murray, and Harris 2011). In our context with satellite imagery, terrain cues might also strongly moderate how we perceive depth; for example, snow is typically the highest part of the terrain, vegetation is more abundant at the bottom of the valleys, and photographic textures allow identification of such features (Çöltekin and Biland 2019; Hartung and Çöltekin 2020).

2.1. Conditions for relief-inversion free image acquisition

While multiple factors moderate depth perception, in our context, where the scene is viewed from the top (aerial perspective), shading and cast shadows are the most important for relief perception. The absence of shadows or their exaggeration can strongly affect relief perception strongly (Abrams 1944; Guerra 2003). In satellite imagery, shadows are perceptual indicators of the position of the sun. Their absence or very limited presence in satellite images, as it occurs at some point in all the points located between the tropics (Figure 5(c)), removes this important depth cue and makes it difficult to perceive relief. In an ideal case, in line with the light-from-above model, the light should come from the north. In the equatorial zone, the sun runs through the NH between 21 March and 21 September (Figure 5(b)); thus, satellite images acquired within this window should have the minimum relief inversion.

Furthermore, the shape-from-shading model suggests that magnitude of the shadows is important. In an ideal case, the elevation angle of the sun should be neither very close to 0° (infinite shadow) nor very close to 90° (null shadow) (Table 1).

Table 1. Shadow factor (f = 1 / tan(α)) or multiplier coefficient applicable to the height of an object to calculate its shadow length based on the angle (α) of the sun's height above the horizon.

Sun elevation angle (α)	0°	15°	30°	45°	60°	75°	90°
Shadow factor: 1/tan(α)	∞	3,73	1,73	1	0,58	0,36	0

Note: The ‘best’ angle and shadow factor in the middle is highlighted with dark gray, gradually getting lighter towards the ‘worst’ angles. Own elaboration.

In addition to the above theories from perceptual psychology, cartographic theory and practice (Imhof (1965) 2007), and recent empirical evidence (Biland and Çöltekin 2017) on SRMs suggest that the light source must have (approximately) an azimuth of approximately 315° and an angle of incidence of 45°. Translating this to acquire satellite images in the equatorial region, we can assume that if the sun is positioned between 30° and 60° above the horizon, the length of the shadows will allow us to observe the relief properly. Outside this range, relief perception may be impaired (Table 1) because the shadows would be very short or very long.

Finally, as mentioned earlier, sun-synchronous satellites orbit the earth between 9:00 am and 11:00 am (Gil et al. 2014). Combining the spatial factors above with this temporal factor, we identified the best theoretical dates for capturing imagery around the equatorial zone (Table 2).

Table 2. Theoretical best spatial and temporal conditions for satellite image acquisition to minimize relief inversion effect at the equatorial region (highlighted dark).

Data source: Motions of the Sun Simulator (2010) (approximated by a tenth of a sexagesimal degree). Own elaboration.

In Figure 6, we present a visual elaboration of the information presented in Table 2 for a specific city in the equatorial zone (Quito) compared to two other cities in the NH (Madrid) and SH (Buenos Aires). Note that the sun never perfectly aligns with an ‘ideal’ position. However, as the sun moves through the NH from March to September, this time window allows for a better image acquisition period than September-March when the sun moves through the SH. Therefore, although the sun is never at the ideal position to avoid relief inversion entirely near the equatorial line, the relief inversion may be weaker or stronger depending on the time of the satellite imagery.

Figure 6. Annual route of the Sun in Quito (Lat.: 0°15´) in polar coordinates (Az, h). Yellow highlighted area shows the annual locus of the sun’s position between 09:00 and 11:00 AM. In S_i (335°, 45°) the ideal location of the Sun proposed in the literature for a correct visualization of the relief. In small, the difference in the situation of the sun in a city of the northern hemisphere and another of the southern hemisphere. Source: Own elaboration based on SunEarthTools (2022) .

To further demonstrate the conditions under which relief inversion may be most or least impaired in the equatorial region, as a proxy, we prepared a series of SRMs showing how relief perception varies based on the changing illumination direction (Figure 7). We created the SRMs shown in Figure 7 based on a digital terrain model. Figure 7 illustrates that as the azimuth of the sun increases (from a to h), the relief changes, with the relief inversion appearing from some intermediate image (variable with personal perceptual characteristics) to the image (h) in which the relief inversion becomes dominant. In this last image, the volcano appears hollow and the river as the crest of a mountain range.

Figure 7. Example SRMs of Sangay river area (i.e. a valley) and Sangay volcano (i.e. a peak) in Ecuador, always at h: 45°. The crater of the volcano (2.0°S, 78.3°N) is marked with a red dot, and the yellow arrows indicate the direction of the sun rays. Yellow outlined SRMs should be perceptually similar to their corresponding satellite images within the recommended time window (09:00–11:00) according to Table 2. Source: Own elaboration.

2.2. Post-processing of satellite images

Because it is not a simple decision to re-route satellite orbits or discard the data that has already been obtained, efforts have been made to remove the relief inversion effect in post-processing, although they all have undesired consequences (Hartung and Çöltekin 2020). Here, we summarize the approaches identified in related works. First, rotating the image by 180° (Saraf et al. 1996) removes the false perception but is not desirable because it goes against the north-up convention in mapping, and thus spatial relationships become confusing (Figure 8(a)). In addition, a more nuanced rotation option may be needed because the illumination angle is not always straight up from north. Second, converting an orthochromatic image to its photographic ‘negative’ (Bernabé-Poveda, Manso Callejo, and Ballari 2005) fixes the problem (Figure 8(b)), but this is impractical because the features become unrecognizable when their color is reversed. Not only does this intervention transform sunny areas into shady areas and vice versa, but the terrain features also appear with gray values that do not correspond to those of real objects. Third, transforming a panchromatic image from the red-green-blue (RGB) system to the hue-saturation-value (HSV) system, and inverting the grays of the intensity channel (I) to later transform back to RGB (Saraf et al. 2007) also appears to help (Figure 8(c)); however, this approach has similar consequences as taking the negative of the image.

Figure 8. Different methods to counter relief inversion. Top row shows the originals, bottom row shows the manipulated images. (a) 180° rotation: north orientation is lost, (b) negative image: snowy patches and the river look black, (c) inverting intensity channels: colors are affected (d) SRM-overlay: original colors are shown through a semi-transparent filter. Source: Own elaboration from Google Maps (Map data: ⓒ 2016 Google, Landsat)

Finally, and most promisingly (Figure 8(d)), overlaying the image with a correctly illuminated shaded relief map (SRM) and adjusting its transparency (Bernabé-Poveda, Sánchez-Ortega, and Çöltekin 2011) solves the problem. Although this appears to be a better solution, depending on the level of transparency/opacity and the colors contained within the original images, it can lead to graying of the resulting images. Such manipulation consistently improves the 3D landform perception but impairs land cover recognition; thus, opacity levels need to be well considered (Hartung and Çöltekin 2020).

In the following sections, we demonstrate the prevalence of the relief inversion effect in satellite images in the equatorial zone based on an empirical experiment. Following the American Psychological Association’s standards in reporting experimental studies, in we first present our Stimuli, i.e. the tested images and the process of their selection (Section 3.1), then we provide information on Participants, i.e. the number, background and additional characteristics (Section 3.2), and we describe the Procedure, i.e. empirical data collection including how the survey was conducted, the tasks and order of actions by the participants (Section 3.3).

3. Our experiments

To quantify and verify the ambiguity of relief perception and prevalence of relief inversion in satellite images taken from the equatorial zone, we designed and conducted two consecutive experiments. Each experiment contained a set of ‘original images’ directly obtained from an online map provider (Google Maps), and a set of 180°-rotated versions of the same images for control and verification purposes. Thus, our main independent variable is the image rotation, that is, the north-oriented vs. 180°-rotated image sets. In the second experiment, we added location as an independent variable because of differences observed in sampling closer to the Equator vs. further away from it (in the southern hemisphere).

The first experiment was designed to be between-subjects to counter the learning effect, but in the following experiment, we switched to a within-subject design with a randomized order to minimize variability among participants. Our main dependent variable was participants’ response accuracy in landform identification in both experiments. We counterbalanced various other factors such as biological sex, location, and order (further elaborated in the following sections), and thus also present exploratory analyses for individual and group differences for image characteristics and participant characteristics. This methodology was consistent with a previous study by Bernabé-Poveda and Çöltekin (2015), which focused on the northern and southern hemispheres (NH and SH) with three stimuli in the equatorial zone. Thus, our findings are directly comparable to those of Bernabé-Poveda and Çöltekin (2015).

The three images in the equatorial zone in Bernabé-Poveda and Çöltekin’s (2015) study were suggestive of a turning point where the clear differences between NH and SH were no longer observable. As three samples from the Equator cannot provide conclusive evidence, building on Bernabé-Poveda and Çöltekin (2015), we examined the prevalence of the terrain reversal illusion in the equatorial zone. Our hypothesis in this study is that relief perception (and inversion) will be more ambiguous in the equatorial zone than in the NH and SH.

3.1. Stimuli

We selected 16 images of rugged terrain on Google Maps containing valleys and ridges and marked six valleys and 12 ridges to be used in the experiments. The orientations of the features are similar. To select the location of the images for our experiment, we considered the countries where the Equator line crosses (Gabon, Congo, Democratic Republic of the Congo, Uganda, Kenya, Somalia, Indonesia, Ecuador, Colombia, and Brazil) (Figure 9).

Figure 9. The equatorial belt. We considered countries that the Equator line crosses for the study before making our selection of the sites. Source: Own elaboration, data: Natural Earth.

We visually examined countries where the Equator line crosses to find regions with rugged terrain, as we observed in a parallel study that subtle changes in elevation might mean more ambiguity in terms of relief inversion (unpublished work). Of the African countries on the list, only Kenya has a landscape rugged enough to clearly perceive relief (Namunyak Wildlife Park area). Other landscapes with relief are covered with woodlands and have only minor terrain changes. The same is true for Malaysia and Indonesia (specifically in Sumatra and Borneo where we collected the stimuli for the study), where relief is relatively subtle or moderate. Colombia and Brazil also did not seem suitable, because they have Amazon forests that occlude relief. Ecuador seemed perfect, as the equatorial line crosses landscapes that have varied relief; thus, we decided to sample images from Ecuador. We selected 16 images (initially nine images, extending the sample with seven more images after a pilot test). We originally sampled images roughly ±1° from the equatorial line, but extended beyond 4° to the south after ambiguous or inconsistent signals from two images bordering 2° to the south (Figure 10). We decided not to extend the study to northern angles because this is well documented in previous work (e.g. our reference study Bernabé-Poveda and Çöltekin 2015).

Figure 10. Approximate locations of the sites of sampled imagery used in the experiments. Images 5 and 6 are highlighted because Experiment 1 revealed ambiguous results for these, leading to sampling more images from south of the Equator line. The images 5 and 6 were used again in Experiment 2 due to regional coherence, and excluded from analysis of Experiment 1 data. In total we analyze the data for 16 images.

We obtained the original images by taking screenshots from Google Maps, and created an alternative set by rotating the originals by 180° as a baseline for verification. More specifically, 180° rotation provides two things: (1) a control condition for the images that are prone to illusion (i.e. does rotating the image change the outcome, if it does, the effect is there, and it is most likely about the illumination direction), (2) previous work showed that rotating images without illusion does introduce the illusion, thus in the equatorial region where we expected high ambiguity it allows us further verify the effect of our stimuli on the outcomes related to phenomenon we study. Additionally, 180°-rotation allows us to make comparisons with previous empirical user studies (e.g. Figure 12).

The selected features (valleys or ridges) were labeled in the images using two (A, B) or three (A, B, C) letters to enable communication with the participants (See Figure 11 for an example).

Figure 11. Example images from the experiment. Letters A and B mark the landform (valley or ridge) that the participants were asked to identify (Map data: ⓒ 2016 Google, Landsat). All images that were used in the experiment are provided in Appendix A.

3.2. Participants

A total of 313 participants (47.9% women, age range 8–50+) participated in the experiment. The first data collection effort was from randomly selected locations in proximity to the Equator (Experiment 1). In Experiment 1, in a between-subjects design, 87 participants (50.6% female, age range 8–50+) responded to our questions with the original images (north-oriented) and 80 participants (50% f) with 180°-rotated images. Pilot testing revealed inconsistencies for two samples (images 5 and 6, near 2°S), thus we conducted an additional data collection campaign for these two images with 72 participants (50% f, age range 8–50+). These results were consistent with those of the first study, leading us to think that there might be a systematic difference. To verify this, we conducted an additional data collection campaign with 74 new participants (40.5% f) using seven new images and their 180°-rotated versions, all sampled from the south of the 2°S (Figure 10, blue dots). Taken together, 87 + 80 + 72 + 74 = 313 participants took part in the experiment (87 + 80 = 167 in Experiment 1 and 72 + 74 = 146 in Experiment 2). The participants had varying levels of education:13.4% primary, 12.8% secondary, 10.9% vocational, and 62.9% tertiary. Age information was collected in brackets, and the distribution of the 313 participants was as follows: 8–15 (15.0%), 16–25 (35.5%), 28–50 (39.6%), and 50+ (9.9%). We also controlled for expertise: 37% of participants had an education that was related to geo/spatial fields (e.g. geography or similar), while 63% had no professional or educational link to geo/spatial domains.

3.3. Procedure

This study was conducted as a set of online experiments using a self-developed (browser-based) questionnaire. Participants were recruited from our network through word-of-mouth. Once participants agreed to participate, we sent them a link to the questionnaire via email. In the same email, participants were informed about the approximate length of the experiment, and that they would consent to the anonymized use of the data for research purposes. Minors (those under 18 years of age) were recruited through their teachers; thus, consent was obtained on their behalf. As mentioned in the previous section, the experiment was conducted over multiple sessions (data-collection campaigns). The first study (Experiment 1) with nine images (and their 180°-rotated versions) yielded issues with two of the ‘extreme’ sampling points (Figure 10, Images 5 and 6) which led to an interim study to double check two of the images, and a second study (Experiment 2) where we added seven more images to the slightly south of the Equator to expand on the observations on points 5 and 6. We decided to analyze the data for points 5 and 6 with Experiment 2 data because of the two distinct location groups that emerged (Equator ±1°, 2–5° South). In all studies, we showed participants one image at a time and asked them the following question: ‘Is the line AB / ABC a ridge or a valley?’ (Figure 11). Participants were intentionally kept naive to the study goals, i.e. they answered the surveys with no information on the motivation of the research and received no suggestions on what to focus on when viewing the images. The participants answered the questions by selecting a binary response (valley or ridge). The study was conducted in Spanish, and the participants voluntarily joined the study without any compensation.

4. Results

4.1. Main effects of location and image rotation

Outlier analysis did not yield extreme cases; thus, we conducted descriptive and inferential statistics. Figure 12 shows the main effects of the two independent variables:180°-rotation, and the two locations studied in Experiment 1 and Experiment 2 (2°–5°south of the Equator).

Figure 12. Main effect of original and rotated images aggregated (a), and split by the main effect of location (b and c) as measured by landform identification accuracy (error bars ±2SE). As we move away from the ±1° of the equatorial line (b) to 2°–5° south (c) the effect vanishes, whereas observations on the northern and southern hemisphere images show a clear reversal (rightmost panel).

The aggregated data for all 16 images (Figure 12(a)) reveal that participants made more mistakes overall with the original images (M_non-rot= 42.6%, SD = 31.5, and M_rot= 59.6%, SD = 33.6), similar to the NH data from Bernabé-Poveda and Çöltekin (2015). Surprisingly, the same pattern holds for Experiment 1 (Figure 12(b)); for the images sampled from ±1°of the Equator, participants made more mistakes with the original images (M_non-rot= 39.1%, SD = 24.1, and M_rot= 85.5%, SD = 15.2). For Experiment 2 (Figure 12(c)), that is, for images sampled from 2°–5°S the difference practically disappeared (M_non-rot= 45.9%, SD = 32.7, and M_rot= 49.4%, SD = 32.7). Inferential analyses confirmed that for Experiment 1, there was an effect of image rotation (Mann-Whitney U = 379, p < .001, r = .777), whereas for Experiment 2, image rotation had no effect (Wilcoxon signed-rank test for related samples Z = .629, p = .531, r = .076). Compared to the SH results from Bernabé-Poveda and Çöltekin (2015), the 2°–5° S also points to an unexpected pattern.

4.2. Main effects of participant characteristics (exploratory)

Since we had a relatively balanced sample in terms of biological sex, age, education, and expertise, we present an exploratory analysis of the main effects of participant characteristics based on their average response accuracy (Figure 13).

Figure 13. Average response accuracy with regards to (a) biological sex, (b) age, (c) education level, and (d) expertise. Error bars: ± 2SEM. None of the factors yielded a statistically significant effect.

4.3. Interactions between the main variables

Next, we analyzed whether the image rotation interacted with participant characteristics separately for Experiment 1 and 2 (i.e. ± 1°of the Equator, 2°–5°south of the Equator). The multifactorial analysis showed that the rotation effect on landform perception was not modified by age, education, or geography-related work experience (Figure 14). The only characteristic that interacted with rotation was the biological sex of the participants, with a low effect size (p = .022, partial eta sq. = .043), and the interaction was only for Experiment 2.

Figure 14. Interactions between image rotation and participant characteristics. For ±1° of the Equator (Experiment 1) accuracy is strongly affected by rotation, whereas for 2°–5° south of the Equator (Experiment 2) there is a significant interaction between biological sex and rotation. * p < .05; *** p < .000. Error bars: ± 2SEM. ⁺ This effect suggests that men bypass the illusion more, but it may be an artifact as it is explained by a single image among the originals, i.e. not for the rotated images (elaborated in the next section).

4.4. Fine grain analysis of individual images

4.4.1. Response accuracy vs. image rotation

Because there are a reasonable number of data points for each image (i.e. > 80 observations per image for Experiment 1 and >70 for Experiment 2), we analyzed participants’ response accuracy for each image separately (Figure 15). The analysis presented in this section was based on categorical data (only right/wrong answers).

Figure 15. Effect of image rotation per individual location presented for each experiment, i.e. participants’ response accuracy in identifying ridges and valleys using original and 180°-rotated images. * p < .05 ** p < .01, *** p < .001.

Putting each location in its spatial context on a map revealed the main effect of rotation at each location (Figure 16). Examining Figure 16, we see a clear agreement for Experiment 1 images at the first location, i.e. ± 1° of the Equator, which yield to same outcomes as NH images despite being at the close proximity of the Equator; whereas in Experiment 2 images at the second location i.e. 2°–5°south of the Equator, exhibit inconsistent results, further suggesting that the illusion is not as strong (or prevalent) in these latitudes.

Figure 16. Effect of image rotation per image in both experiments. We also marked the direction of sunlight per image as identified from the image metadata at the time of satellite flight.

4.4.2. Response accuracy: biological sex vs. rotation

Because we observed an interaction effect between biological sex and response accuracy in Experiment 2, we further analyzed each image separately and split by biological sex (Figure 17).

Figure 17. Effect of rotation among biological sex groups.

Figure 17 shows that for the majority of images in Experiment 1, rotating the image improves the accuracy for both biological sex groups. In Experiment 2, for images 10, 14, 15, and 16, rotation impaired accuracy only among men, whereas women were not affected by rotation. Image 12 was somewhat special, as both men’s and women’s accuracy was clearly improved with the rotated image, possibly due to a pronounced landform and an easy-to-recognize river in the scene (Appendix A).

Details of the statistical analyses have been provided in Appendix B. Figure 18 shows the results in their spatial context.

Figure 18. Effect of rotation for all participants (shown with colors of squares) and among biological sex groups (shown with arrows).

5. Discussion and conclusions

The relief inversion effect is a visual illusion that affects three-dimensional perception. It is a well-documented phenomenon in perceptual psychology and is related to a cognitive bias related to overhead illumination (e.g. Berbaum, Bever, and Chung 1984; Kleffner and Ramachandran 1992). It is also well documented in shaded relief maps (e.g. Imhof (1965) 2007; Saraf et al. 1996; Bernabé-Poveda, Manso Callejo, and Ballari 2005; Biland and Çöltekin 2017). Interestingly, it also occurs in images where the main depth cue is shadows, especially if the images are orthogonal, the southern slopes are illuminated, and the image is displayed north-up by convention. The prevalence of the effect is clearly shown by Bernabé-Poveda and Çöltekin (2015), who demonstrated that images from the Northern Hemisphere (NH) were much more likely to be prone to this illusion than images from the southern hemisphere (SH), whereas they sampled three images from the Equator, which appeared to suggest some ambiguity. Besides the three data points presented by Bernabé-Poveda and Çöltekin (2015), to the best of the authors’ knowledge, the equatorial region has never been systematically examined. In this paper, we present a study that fills this gap.

Our original hypothesis was that the images sampled from the Equatorial region would be more often ambiguous, that is, there would be less agreement between the participants whether a linear landform was a valley or a ridge. In our first study (Experiment 1), we did not see the expected pattern; in fact, for the majority of the samples, there is a strong agreement among the participants that the samples exhibit the same pattern as in the NH, that is, the illusion is strong in the original images, and disappears when the images are rotated (as the light comes from ‘above’ after the images are rotated, and shadows are where they are supposed to be, i.e. on the southern slopes). However, this agreement among the participants was true only for images from ±1° of the equatorial line. The study contained two images close to 2°S which demonstrated more ambiguity and led to new data collection campaigns.

After an interim study verifying that these two images were indeed causing ambiguity, we collected more data on image samples between 2° and 5° south of the Equator to examine if the hypothesized ambiguity might be occurring somewhat more south of the Equator than ±1°of the equatorial line. A second study (Experiment 2) with samples collected from to 2°–5° south of the Equator revealed that there may be a turning point where the effect of natural light shifts from illusion-free (SH) to ambiguous (2°–5° south of the Equator) and illusion-prone (±1°of the equatorial line and the NH).

While this observation is consistent with the observations documented in the shaded relief maps (Biland and Çöltekin 2017), it is surprising that the ‘turning point’ is not at the Equator but rather somewhat more south of it. We examined whether land cover cues (presence of snow, rivers, etc.) or a convexity bias (Hill and Johnston 2007) might affect the results, but our examinations suggest that these do not confound the outcomes. We do not have a clear explanation for why this may be happening. One interpretation is that this result can be partly explained by the temporal windows in which the analyzed satellite images were taken. In the period from September to March, the Sun runs south of the E-W line, which is the position that leads to more relief inversion. However, this interpretation does not account for ambiguity (or mixed results regarding the agreement among participants). Another interpretation might be that, while the Equator line is simply the geometric middle between the two polar regions, it is possible that this is not the ‘middle’ from the perspective of where the illumination hits the Earth, and thus the slopes of mountain ranges more from the top compared to SH and NH. This proposition needs more evidence, as we cover a small region in this study (sampled data were only from Ecuador for pragmatic reasons). Future studies where data is collected from further south, and from other parts of the world around this belt, would be useful to verify if the ‘turning point’ really lies around 2°–5° south of the Equator, or perhaps even more south since we did not expand further than ∼5° S.

For control purposes, we counterbalanced the participants for biological sex and asked them about their age, education level, and expertise. These variables were not controlled for between-group factors (i.e. we did not recruit an equal number of experts in all age, education, or biological sex groups). Nonetheless, we conducted an exploratory analysis to examine group differences as the groups were reasonably balanced. The main effects split by location regarding biological sex first suggest that overall, men are more likely to bypass the illusion as the ambiguity grows (not in ±1°of the equatorial line, but only in the rotated images of the to 2°–5° south of the Equator). However, a deeper analysis showed that this may be an artifact of a single image. Under the same conditions, descriptive statistics suggest that in the majority of images, men have a somewhat stronger illusion, whereas women have similar outcomes for original and rotated images. Given the mixed results, we believe, in essence, that there are no justifiable differences based on biological sex regarding the prevalence of the illusion (as also documented in previous work e.g. Biland and Çöltekin 2017; Çöltekin and Biland 2019). Descriptive statistics regarding age suggest that the youngest participants might bypass the illusion more than the older age groups, but this too is not statistically significant and is likely due to chance. Unlike previous work (Bernabé-Poveda and Çöltekin 2015; Çöltekin and Biland 2019), we did not observe differences based on expertise. Thus, we conclude that the main effect of location appears to be true despite any individual and group differences; that is, our observations hold across age, expertise, education, and biological sex groups. A future study that studies individual and group differences more systematically might still be interesting to examine if the faint signals detected in the descriptive signals in our study have merit. In these experiments, participants were kept naive to the goals of the study. A future study could further explore whether the accuracy outcomes would be different should they know about the phenomenon, i.e. if people try, could they bypass the illusion. Anecdotal experiences of the authors suggest that similarly to other optical illusions knowing about the illusion’s presence does not change the experience, however this observation is not fully empirically verified.

An additional qualitative observation is that, unlike in the NH and SH, we see a strong variation depending on the illumination (sunlight) direction (which is implicitly linked to the time of the year, and time of the day) in the images. Following the ‘light-from-above’ model (which is in accordance with the cartographic tradition of relief representation), the most suitable annual season to avoid pseudo-relief in the equatorial strip is when the Earth is closer to the sun, that is, during the summer solstice. When the Sun is on or near the E-W line (dates near the equinoxes), relief and pseudo-relief appear equally frequently in both the direct and rotated images.

With the wide availability of satellite images in almost all map providers today, it is not only interesting from a fundamental science perspective in which we better understand the conditions relief inversion illusion occurs, and what might be the implication of that for the geographic knowledge, but it is also important that we are aware which images are perceptually ‘trustworthy'. We believe, thus, that our study contributes to both the fundamental and applied research goals.

Acknowledgements

We would like to thank all the participants of the two reported experiments. We also want to thank Dr Adrian Ochtyra (University of Warsaw) for her help in satellite images interpratation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon request.

Additional information

Funding

This work was supported by two funding sources: 1) CYTED (Science and Technology for Development) within the Network “IDEAIS: Intelligent Assistants for Spatial Data Infrastructures” (Grant Number 519RT0579), and 2) Google: [Grant Number 2014_R2_742].

Appendix A

Appendix B.

Detailed statistical analyses.

Table B1. Chi-square goodness of fit test comparing participants’ response accuracy with original (non-rotated) GoogleMap images vs. their 180°-rotated versions.

	N° of Image	Response accuracy		Χ^2	ϕ	df	p
		Non-rotated	Rotated
Experiment 1	1	32.2	86.3	50.0	.55	1	.000***
	2	47.1	92.5	40.0	.49	1	.000***
	3	46.0	93.8	44.4	.52	1	.000***
	4	37.9	81.3	32.3	.44	1	.000***
	7	50.6	93.8	37.9	.48	1	.000***
	8	32.2	63.8	16.7	.32	1	.000***
	9	27.6	97.5	60.8	.60	1	.000***
	N° of Image	Response accuracy		McNemar's test	df	p
		Non-rotated	Rotated
Experiment 2	5	43.05	52.78	.80	1	.371
	6	37.50	50.00	1.83	1	.176
	10	74.3	48.6	8.757	1	.003**
	11	37.8	35.1	.033	1	.855
	12	31.1	82.4	31.114	1	.000***
	13	48.6	54.1	.205	1	.651
	14	63.5	41.9	5.297	1	.021*
	15	40.5	29.7	1.114	1	.291
	16	63.5	40.5	5.953	1	.015*

Table B2. Chi-square goodness of fit test comparing participants’ response accuracy with original (non-rotated) GoogleMap images vs. their 180°-rotated versions for males and females.

	N° of image	biological sex	response accuracy		χ^2	ϕ	df	p
			Non-rotated	Rotated
Experiment 1	1	f	30.2	92.5	33.5	.64	1	.000***
		m	34.1	80.0	17.9	.46	1	.000***
	2	f	39.5	95.0	28.5	.59	1	.000***
		m	54.5	90.0	12.9	.39	1	.000***
	3	f	39.5	92.5	25.6	.56	1	.000***
		m	52.3	95.0	19.2	.48	1	.000***
	4	f	41.9	75.0	9.3	.34	1	.002**
		m	34.1	87.5	24.8	.54	1	.000***
	7	f	55.8	95.0	16.8	.45	1	.000***
		m	45.5	92.5	21.3	.50	1	.000***
	8	f	32.6	67.5	10.1	.35	1	.001***
		m	31.8	60.0	6.7	.28	1	.010**
	9	f	30.2	87.5	27.9	.58	1	.000***
		m	25.0	87.5	33.0	.63	1	.000***
	N° of image	biological sex	response accuracy		McNemar’s test	df	p
			Non-rotated	Rotated
Experiment 2	5	f	38.9	52.8	.842	1	.359
		m	47.2	52.8	.038	1	.845
	6	f	33.3	47.2	1.231	1	.267
		m	41.7	52.8	.409	1	.523
	10	f	63.3	53.3	.308	1	.581
		m	81.8	45.5	9.38	1	.002**
	11	f	26.7	33.3	.083	1	.774
		m	45.5	36.4	.500	1	.481
	12	f	20.0	80.0	14.45	1	.000***
		m	38.6	84.1	15.04	1	.000***
	13	f	23.3	56.7	5.06	1	.021*
		m	65.9	52.3	.89	1	.345
	14	f	63.3	50.0	.563	1	.454
		m	63.6	37.2	4.76	1	.027*
	15	f	30.0	43.3	.563	1	.454
		m	47.7	20.5	4.32	1	.038*
	16	f	53.3	50.0	.000	1	.999
		m	70.5	34.1	8.65	1	.003**

Note: Statistically significant results are marked bold.