自动日光与天光基础图像分解方法
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"本文主要探讨了在增强现实技术中如何实现虚拟对象与真实环境的光影一致性的关键问题，即户外延时视频的基本图像分解。通过这种方法，可以计算出静态室外场景在太阳光和天空光作用下的全局光照效果的基础图像，以确保虚拟对象的光照效果与真实世界同步变化。该方法自动化程度高，且不受物体反射率理想漫射或特定天气条件（如阴天或晴天）的限制。其工作流程包括使用k-means聚类算法识别阴影像素，然后通过迭代解算阳光和天空光的基础图像，并利用基础图像的约束和先验条件进行优化。实验结果验证了方法的效能和适应性，不仅适用于增强现实，还可应用于图像理解和压缩领域。"
在这篇研究中，作者提出的是一种用于处理户外延时视频的新方法，目标是解决在增强现实应用中的光照一致性问题。他们提出的基础图像分解技术旨在从时间序列图像中提取场景的太阳光和天空光基础图像，这些基础图像能够体现场景的几何特性和材质反射率。这样的分解对于实现虚拟对象在真实环境中的无缝融合至关重要，因为虚拟对象的光照效果必须与实际环境相匹配。
该方法的一大优势在于其全自动特性，与以往的方法相比，它不依赖于物体反射率为理想漫射或者特定天气条件（如阴天或晴天）的假设。这一创新意味着它能适应更广泛的现实场景，提高了方法的普适性。在实际操作中，首先通过k-means聚类算法对像素的延时曲线进行分析，识别出阴影区域，随后运用迭代算法解算阳光和天空光的基础图像。此外，为了进一步优化结果，他们会利用基础图像的内在约束和先验知识。
实验结果显示，这种新的基础图像分解方法能够有效地捕获场景的光照变化，并且具有良好的灵活性。这表明该方法不仅可以用于增强现实技术，还可以应用于图像理解和压缩等其他领域，拓展了其潜在的应用范围。
这篇文章揭示了在增强现实背景下，处理户外场景光照变化的关键技术和方法，对于提高虚拟与现实融合的视觉质量有着重要的理论和实践意义。通过自动化的图像分解，该方法可以适应各种复杂的户外环境，确保虚拟对象在任何光照条件下都能自然地融入真实世界。
Basis image decomposition of outdoor time-lapse videos
The dominate light in outdoor scenes is the sunlight and
the skylight, and the skylight is distributed on the sky dome.
Since both the sunlight and skylight are far away from the
scenes, it is reasonable to assume that the lighting condition
are the same for each object in the view. We take no account
on any other artificial light sources.
3 Previous model
The global illumination of any scenes can be modeled by
Kajiya’s rendering equation [5]. Radiance of an object is
recorded as RGB value of pixels by CCD of a camera [4],
which are modulated by scale. Therefore, the following
analysis are performed in radiance space.
We adopt the following rendering equations:
L(x, ω, λ, t) = E(x,ω,λ,t)
+
Ω
ρ(x,ω
,ω,λ)S(x,ω
)L(x, ω
,λ,t)
×cos θ(x,ω
)dω
, (1)
where x is an observed point, λ denotes the wavelength of
the light, t is time, ω and ω
are reflection and incident ray
direction, respectively, E(x,ω,λ,t) is the emission light in-
tensity, Ω is the sphere or hemisphere of the incident light,
and ρ(x,ω
,ω,λ) is the BRDF at point x from direction
ω
to ω, and S(x,ω
) is occlusion function, L(x, ω
,λ,t) is
the incident light at x from direction ω
, θ(x,ω
) is angle
between the incident light and the normal at point x.This
equation expresses multiple interreflection among surfaces
and the light arrived at the camera may be reflected arbitrary
times in the scenes.
Liu et al. [11] once proposed a decomposition model of
basis images, by ignoring the interreflection among objects,
and assuming that the sky light is uniformly distributed with
linear HDR function; it arrives at a linear decomposition
equation as follows:
I =E ·C (2)
where I stands for the input images captured with a fixed
camera, E stands for the sunlight and the skylight radiance,
and C is the images of the scene accounting for only the
direct illumination of sunlight and skylight and they are de-
fined as following:
C
sun
(x,λ,t)=
Ω
sun
ρ(x,ω
,ω,λ)S(x,ω
)
×cos θ(x,ω
)dω
,
C
sky
(x,λ,t)=
Ω
sky
ρ(x,ω
,ω,λ)S(x,ω
)
×cos θ(x,ω
)dω
,
(3)
where ω is removed from C
sun
and C
sky
due to fixed cam-
era and geometry in the scene. This model is unsuitable for
the cases of interreflection and non-diffuse surface. In this
paper, we derive the decomposition model in another way.
4 Linear decomposition model
4.1 Global illumination model with interreflection
Based on our assumption, we have E(x) =0 for all pixels of
object surface. A global illumination model should account
for all levels of interreflectance in the scene. We will show
that the linearity is kept for the global illumination model
if the radiance distribution of an area light source is up to
scale.
The rendering equation evaluates the interreflection
through recursive light transfer. An equivalent simulation
is to classify the rays according to the levels of inter-
reflectance. The first level of illumination is by the direct
light source, and then those illuminated surfaces become
light sources of the second level accounting for interreflec-
tion, and so on. Different levels of interreflections proceed
infinitely and they are accumulated as follows:
L(x, ω, λ, t) =
∞
k=0
L
(k)
(x,ω,λ,t) (4)
where k denotes the level of the inter-reflection of light,
L
sun
(x,ω,λ,t) and L
sky
(x,ω,λ,t) integrate all levels of
the inter-reflection of light source. Specifically, according to
rendering equation for each layer of interreflection, we have:
L
(0)
(x,ω,λ,t)=E(x,ω,λ,t),
...
L
(k+1)
(x,ω,λ,t)=
Ω
ρ(x,ω
,ω,λ)S(x,ω
)
×L
(k)
(x, ω
,λ,t)cos θ(x,ω
)dω
.
(5)
From these equations, we can derive the linear property of
decomposition equation.
4.2 Linearity of global illumination
The input images of an outdoor scene are captured at a fixed
viewpoint. For the moment, we assume that the scene is
static, the reflectance of scene points is not limited to Lam-
bertian, but the irradiance of any scene point is entirely due
to natural light.
We assume that the geometry of the scene, the camera po-
sition and orientation, the distribution of the incident light,
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