Real-time rendering of aerial perspective effect based on turbidity estimation
- Carlos Morales^{1}Email author,
- Takeshi Oishi^{1} and
- Katsushi Ikeuchi^{2}
https://doi.org/10.1186/s41074-016-0012-1
© The Author(s) 2017
Received: 28 July 2016
Accepted: 13 December 2016
Published: 13 January 2017
Abstract
In real outdoor scenes, objects distant from the observer suffer from a natural effect called aerial perspective that fades the colors of the objects and blends them to the environmental light color. The aerial perspective can be modeled using a physics-based approach; however, handling with the changing and unpredictable environmental illumination as well as the weather conditions of real scenes is challenging in terms of visual coherence and computational cost. In those cases, even state-of-the-art models fail to generate realistic synthesized aerial perspective effects. To overcome this limitation, we propose a real-time, turbidity-based, full-spectrum aerial perspective rendering approach. First, we estimate the atmospheric turbidity by matching luminance distributions of a captured sky image to sky models. The obtained turbidity is then employed for aerial perspective rendering using an improved scattering model. We performed a set of experiments to evaluate the scattering model and the aerial perspective model. We also provide a framework for real-time aerial perspective rendering. The results confirm that the proposed approach synthesizes realistic aerial perspective effects with low computational cost, outperforming state-of-the-art aerial perspective rendering methods for real scenes.
Keywords
Real-time rendering Aerial perspective Shader programming1 Introduction
In real open-air scenes, when a target object viewed by an observer is far, the perceived object’s appearance changes, being fainted and blended to the environmental light color. This natural effect is known as aerial perspective and is due to the light scattering by particles suspended in the atmosphere.
In general, we have to render an artificial aerial perspective effect on a target object to emulate the natural atmospheric effect. This goal is specially more difficult in real-time applications in outdoor scenes, which present a challenge due to the variant illumination and atmospheric conditions such as clear, hazy, or cloudy days.
A conventional approach for aerial perspective rendering is to find an outdoor light scattering model with parameters that lead to generate a realistic synthesized look according to the real scene. Such scattering models can be analyzed from captured skies using sky illumination models [1–7]. Due to its simplicity and accuracy for scattering modeling, a heuristic parameter called turbidity (T) has been used to categorize atmospheric conditions [8–12]. Following that approach, we propose a full-spectrum turbidity-based aerial perspective model that enables us to render realistic aerial perspective effects in real time. Our model heavily relies on estimating turbidity from clear-sky regions of a captured omnidirectional sky image. Thus, scenes where the sky is not visible are beyond the scope of this work.
- 1)
Turbidity estimation: The captured omnidirectional sky image is compared with turbidity-based sky models to find the turbidity value that provides the best matching (Section 3.4).
- 2)
Aerial perspective rendering: An improved turbidity-based scattering model (Section 5) is used in a full-spectrum aerial perspective rendering equation (Section 4) to generate the final synthesized scene. This stage is performed in real time in a graphics processing unit (GPU) framework (Section 6).
- 1)
Improved turbidity-based scattering model for rendering that fit to real atmospheric effects more accurately than previous works [3, 13].
- 2)
A novel full-spectrum, turbidity-based aerial perspective rendering model that synthesizes plausible aerial perspective effects in real scenes and improves over previous works [13–15] in terms of visual coherence.
- 3)
A real-time framework for aerial perspective effect rendering. The implementation delivers more than two orders of magnitude speed-up compared to prior art [13], allowing real-time performance needed in applications such as MR.
2 Related work
Previous methods for aerial perspective modeling and rendering rely on understanding the scattering phenomena in the atmosphere. McCartney [16] presented an excellent review of former works on atmospheric optics. His work contains relevant data about the scattering phenomena under different weather conditions categorized by the heuristic parameter turbidity (T). T is used to model the scattering by molecules of air and larger particles, such as haze, and is employed for classifying various atmospheric conditions ranging from pure air to fog. Since the atmospheric phenomenon in [16] is modeled using real data, it has been used in both CV and CG fields. However, such models have been used differently, varying depending on whether the aim is oriented to CV or CG.
2.1 CG-oriented aerial perspective rendering
In this category, the atmospheric optics models are targeted for completely virtual scenes. Preetham et al. [3] presented a full-spectrum turbidity-based analytical sky model for various atmospheric conditions. Based on that model, they developed an approximated scattering model for aerial perspective rendering. Dobashi et al. [17] introduced a fast rendering method to generate various atmospheric scattering effects via graphics hardware. Nielsen [18] presented a real-time rendering system for simulating atmospheric effects. Riley et al. [19] presented a lighting model for rendering several optical phenomena. Schafhitzel et al. [20] rendered planets with atmospheric scattering effects in real time. Bruneton and Neyret [5] rendered both sky and aerial perspective from all viewpoints from the ground to outer space.
The synthesized atmospheric effects generated by the mentioned works are visually plausible in fully CG scenes where the illumination is controlled. However, their direct implementation in real scenes does not have a similar performance, since the scattering models need to be tuned to fit the variant, natural outdoor illumination. Moreover, such models are usually targeted as post processing effects where visual quality is more important than computational cost.
2.2 CV-oriented aerial perspective rendering
This group of methods model the atmospheric phenomenon in real outdoor scenes. Using scattering models, several works were able to restore captured images at different weather conditions. Gao et al. [21] presented an aerial perspective model for haze filtering based on a parameter called maximum visibility. Zhu et al. [15] developed a linear color attenuation prior for image de-hazing based on a parameter called scattering coefficient. The synthesized results from these works successfully corrected and restored at some extent the color of images under hazy conditions. However, these methods are not automatic and the results depend on manual tuning of either the maximum visibility in [21] or the scattering coefficient in [15], which control the amount of de-hazing.
Automatic image restoration approaches have also been proposed in the literature. Narasimhan and Nayar [22] proposed a physics-based scattering model to describe the appearances of real scenes under uniform bad weather conditions. Using that scattering model, their method restored the contrast of one image; nonetheless, their method required a second image of the same scene under a different weather condition. This limitation was overcome by He et al. [14], who proposed an automatic haze-removal approach for single images using a dark channel as prior. Results in [14] showed consistent and fast image de-hazing. However, using their method for aerial perspective rendering leads to appearances that are inconsistent with natural aerial perspective, especially in cases with high haze densities.
To solve the previous drawbacks, Zhao [13] proposed an automatic turbidity-based aerial perspective model. In his approach, turbidity was estimated from captured omnidirectional sky images. The camera’s spectral sensitivity was estimated for conversion from spectral radiance to RGB pixel values. Combining the estimated spectral sensitivity and a simple correction of Preetham’s scattering model [3], his method was able to generate an aerial perspective effect over virtual objects for outdoor MR. However, his method makes the appearance of the synthesized virtual object suffer from a strong aerial perspective effect even for low turbidity values at short distances. Moreover, his approach has a high computational cost.
3 Preliminary
3.1 Aerial perspective modeling
where β _{R} is the Rayleigh scattering coefficient that analyzes particles much smaller than λ, such as molecules of air, and β _{M} is the Mie scattering coefficient that models particles whose size is nearly equal to λ, such as particles of haze.
where n=1.0003 is the refractive index of air in the visible spectrum, N=2.545×10^{25} m^{−3} is the molecular number density of the standard atmosphere, p _{ n }=0.035 is the depolarization factor for air, h is the altitude at the scattering point, H _{R0}=7994 m is the scale height for the Rayleigh scattering, c(T) is the concentration factor that depends on the atmospheric turbidity, ν=4 is the Junge’s exponent, K(λ) is the wavelength-dependent fudge factor, and H _{M0}=1200 m is the scale height for Mie scattering.
3.2 Atmospheric condition via turbidity
where h _{i} and h _{f} are the initial and final altitudes of the optical path, respectively.
3.3 Rendering equation
where L(λ) is the reflected spectral radiance at the object surface, the range 380 to 780 nm stands for the visible spectrum of light, and q _{c}(λ) is the spectral sensitivity of the camera.
The camera’s spectral sensitivity is important for color correction since it compensates the effects of the recording illumination. In this matter, we benefited from Kawakami et al. [28] and the public data of spectral sensitivity for various cameras [29]. They estimated q _{c}(λ) from omnidirectional captured sky images and turbidity-based sky spectra.
3.4 Atmospheric turbidity estimation
where N is the number of sample points used in the calculation process. In this paper, we solve for the turbidity using the Levenberg-Marquardt algorithm (LMA), a simpler yet efficient approach compared to the particle swarm optimization used in [13].
Since the Preetham sky model does not provide equations for calculating the brightness of cloudy pixels, the Random Sample Consensus (RANSAC) approach is used to remove cloudy pixels (outliers) from the sampling and estimate turbidity only from clear-sky pixels (inliers).
4 Aerial perspective rendering equation
where L(0,λ), L(∞,λ), β _{sc}(·), and s are same as in Eq. (1) and h _{0} is the altitude at the observer position.
5 Improved scattering model for rendering
Scattering models for real scenes require parameters that guarantee a realistic result when rendering the aerial perspective effect. For this purpose, we propose an improved scattering model based on real data of [16] about weather conditions via scattering coefficients, which is summarized in Table 2 of the Appendix. The data in [16] was measured under standard conditions, which is using a spectrally weighted average wavelength (λ=550 nm) for daylight within the visual spectrum at sea level (h=0 m).
5.1 Rayleigh scattering coefficient correction
where n, N, p _{ n }, and H _{R0} are the same as in Eq. (3), h _{0} is the altitude at the observer, and K _{R} is given by Eq. (14).
5.2 Mie scattering coefficient correction
where \(\hat {c}\) is given by Eq. (16), ν and H _{M0} are the same as in Eq. (4), h _{0} is the altitude at the observer, and K _{M} is given by Eq. (17).
6 GPU implementation of the aerial perspective rendering
Nowadays, GPU implementation is common in CV and CG. Given the proposed aerial perspective model, we now present how to implement it on a GPU. First, we show the GPU rendering pipeline that includes both a general rendering pipeline and our proposed fragment shader. Then we explain the fragment shader in more detail.
6.1 GPU rendering pipeline
In MR applications, we denote VO for the virtual object and BG for the background to which the virtual object is merged. In case of composition applications, the input image is considered as VO, while there is no BG. Without lost of generality, we explain the rendering pipeline only for the MR case.
In general, raw vertices and primitives of a VO inputted to a vertex shader are processed and transformed for a rasterizer. The rasterizer scans and converts the transformed primitives into 3D fragments, which are then processed in the default fragment shader and merged to obtain textured and lighten 2D fragments. Normally, the resulting 2D fragments are stored in a default frame buffer and then go to the display. We propose to employ one off-screen frame buffer for storing the 2D fragments of the VO coming from the default fragment shader and another off-screen frame buffer for storing the captured real scene that we will call BG. Since the aerial perspective rendering of Eq. (10) is an RGB-based model, we implement it on a GPU at a fragment level. We insert the fragment shader between the two off-screen buffers and the default frame buffer in order to render a MR frame where the VO has a synthesized aerial perspective effect seamlessly to the natural atmospheric effect visualized on BG.
6.2 Proposed GLSL fragment shader
- 1)
Initialization: The program calls the textures I _{VO} and I _{BG}, the target’s relative depth \(\bar {s}\in \,[\!0,1]\) and position (l _{x},l _{y}) in 2D screen coordinates, the turbidity T, and the spectral sensitivity q _{c}.
- 2)Positioning: The target’s absolute position in world coordinates is estimated by$$ s = {s}_{\text{near}}/(1-\bar{s}(1-{s}_{\text{near}}/{s}_{\text{far}})), $$(19)$$ \phi = \arctan(y/x), $$(20)$$ \theta = \arccos(z / \sqrt{x^{2}+y^{2}+z^{2}}), $$(21)where the depth s is in meters; s _{near} and s _{far} are the distances of near and far planes, respectively; and (x,y,z) is the target’s relative position in world coordinates computed from$$ \left[ \begin{array}{c} x \\ y \\ z \\ w \end{array} \right] = [M_{4\times 4} \times P_{4\times 4} \times \mathrm{R}_{4\times 4}]^{-1} \left[ \begin{array}{l} l_{\mathrm{x}} \\ l_{\mathrm{y}} \\ \bar{s} \\ 1 \end{array} \right], $$(22)where M and P are the model view matrix and the projection matrix, respectively, and R is the remap matrix given by$$ {R}_{4\times 4} = \left[ \begin{smallmatrix} 2 & 0 & 0 & -1 \\ 0 & 2 & 0 & -1 \\ 0 & 0 & 2 & -1 \\ 0 & 0 & 0 & 1 \end{smallmatrix} \right]. $$(23)
- 3)
Aerial perspective rendering: The attenuation factor Γ _{c}(T,s) is computed using Eq. (11). \(I^{\infty }_{\mathrm {c}}(T, \phi, \theta)\) is computed according to Eqs. (12) and (13). The target with aerial perspective effect \(\hat {I}_{\text {VO}}\) is calculated using Eq. (10) and then blended with I _{BG} to produce the final result.
7 Experimental results
In this section, we evaluated the turbidity estimation approach and the aerial perspective rendering model. Composition application was used for qualitative and quantitative evaluation of the method. We also provide an application on mixed reality. All the following experiments were run on C++ on a PC with OS: Windows 7; CPU: Corei7 2.93 GHz; RAM: 16 GB; GPU: nVIDIA GTX 550 Ti 4049 MB.
7.1 Turbidity estimation test
We tested our approach for turbidity estimation using static omnidirectional images of both simulated skies and captured skies.
7.1.1 Evaluation with sky models
Estimated turbidity values using the Preetham sky models as an input image
T _{sky model} | \(\bar {T}\) | σ _{ T } |
---|---|---|
2.0 | 2.011791 | 0.004660 |
3.0 | 2.851666 | 0.027230 |
4.0 | 4.241544 | 0.043840 |
5.0 | 4.992700 | 0.055292 |
6.0 | 5.836839 | 0.061853 |
7.0 | 7.138090 | 0.062630 |
8.0 | 8.010996 | 0.135764 |
9.0 | 9.099154 | 0.089461 |
7.1.2 Evaluation with captured sky images
7.2 Aerial perspective model evaluation
7.2.1 Evaluation of the scattering coefficients
where \(\hat {\beta }_{\text {M1}}\) and \(\hat {\beta }_{\text {M2}}\) refer to our improved Mie scattering coefficient for turbidities T _{1} and T _{2}, respectively. Considering a turbidity of 1.6 for an exceptionally clear atmospheric condition, we plotted Fig. 10 using Eq. (24).
7.2.2 Airlight evaluation
We performed a qualitative evaluation of the airlight constituent of real images using our rendering model of Eq. (10). Real scenes of Tokyo city were captured using Canon EOS5D. The experiments aim to show performance using a single image as input. Because of this, we used Google earth to manually estimate a rough depth map of the scenes. Nonetheless, depth maps can be estimated either from two images of the same scene at different weather conditions using the proposed aerial perspective model or from single images using approaches as in [14, 15]. For a fair evaluation and comparison with state-of-the-art approaches [13–15], the input images were manually segmented to only apply aerial perspective effect over the scene excluding the sky. In addition, the parameters used in the mentioned approaches were set to be optimal.
Moreover, due to the attenuation factor, the more distant the target object is, the more similar to the environmental illumination color the airlight should be. Certainly, observing the far way mountains in Fig. 11 we notice that our airlight also followed that theoretic definition, while [13–15] did not succeed to do so.
7.2.3 Evaluation of the aerial perspective effect
In the evaluation, we used the input image with T _{s}=1.9 of Fig. 11 as the source image since it provides more detailed color information than scenes with higher turbidities. We targeted to ground truth images with T _{t}={2.11, 2.54, 2.94, 4.36}.
where H is histogram, \(\bar {H}\) stands for the histogram mean, c ∈{H-S,V}, and lower indexes 1 and 2 correspond to \(\hat {I}_{\mathrm {t}}\) and I _{t}, respectively. In both the HSV correlation and the SSIM index metrics, a higher value represents a higher similarity between the synthesized aerial perspective and the ground truth.
The quantitative results showed that our approach outperformed the methods mentioned beforehand. It is worth noting that while [14] had a better SSIM index than ours only at the least hazy scene, our method provided the highest combined HSV histogram correlation for all scenes. In general, at lower turbidities, [14] rendered compelling results closer to ours than [13, 15]. However, contrary to our method, the quality of [13–15] drastically decreased as the haze became denser.
7.3 Application on MR
We applied the aerial perspective effect to a CG model rendered in a real scene. For convenience of the experiment, we employed a fixed view in order to avoid occlusion and tracking issues and focus on the appearance issue. However, this feature is not a limitation since the fixed view issue can be handled using conventional tracking systems. The altitude at the observer position was h _{0}=40 m above sea level. The distance from the CG model to the observer was around 3500 m. The real scenes of the experiments correspond to the scenes captured for the turbidity estimation test seen in Fig. 8. We use the real scenes with estimated atmospheric turbidities of 1.9, 2.10, 2.94, and 4.36.
8 Conclusions
We have proposed an efficient turbidity-based method for aerial perspective rendering in real scenes. The atmospheric turbidity is effectively estimated by matching the luminance distributions of a sky model and an omnidirectional captured sky image. An improved scattering model was deduced using real data to classify scattering coefficient values via turbidity. The enhanced scattering model was employed to provide a novel full-spectrum aerial perspective rendering model. Qualitative and quantitative evaluations on real and synthesized data show that the rendering method accomplishes realistic appearances seamlessly to the natural aerial perspective in real time, outperforming related works in terms of appearance quality and computational cost.
9 Appendix
Table 2 corresponds to the classification of weather conditions based on scattering coefficients. The data was adapted from [16], where measurements were carried out under standard conditions. Standard conditions refer to a spectrally weighted average wavelength (λ=550 nm) for daylight within the visual spectrum at sea level (h=0 m).
Weather conditions via scattering coefficients
Weather condition | β _{R} (km ^{−1}) | Min β _{M} (km ^{−1}) | Max β _{M} (km ^{−1}) |
---|---|---|---|
Pure air | 0.0141 | 0 | 0 |
Exceptionally clear | 0.0141 | 0 | 0.0639 |
Very clear | 0.0141 | 0.0639 | 0.1819 |
Clear | 0.0141 | 0.1819 | 0.3769 |
Light haze | 0.0141 | 0.3769 | 0.9399 |
Haze | 0.0141 | 0.9399 | 1.9459 |
Fog | 0.0141 | 1.9459 | More than 78 |
Declarations
Acknowledgements
This work was, in part, supported by JSPS KAKENHI Grant Number 16H05864.
Authors’ contributions
CM, TO, and KI designed the study, developed the methodology, and performed the analysis. CM collected the data. CM wrote the manuscript, and TO and KI helped to polish it. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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