High Dynamic Range Imaging.

High Dynamic Range Imaging

High Dynamic Range [3] In photography, dynamic range (DR) is measured in exposure value (EV) differences or stops, between the brightest and darkest parts of the image that show detail.

HDR imaging [4] HDR imaging: this may involve shooting digital images at different exposures and combining them selectively to retain detail in light and dark areas despite the limited dynamic range of the sensor array. An example of a wide dynamic range image, and the two different images it is created from, the short exposure image and the long exposure image.

Tone Mapping [3] Tone mapping: this reduces overall contrast to facilitate display of HDR images on devices with lower dynamic range (LDR), can be applied to produce images with preserved or exaggerated local contrast for artistic effect. Simple contrast reduction Local tone mapping

Brightness and Intensity Value [1] When we photograph a scene, either with film or an electronic imaging array, and digitize the photograph to obtain a two-dimensional array of brightness values, these values are rarely true measurement of relative radiance in the scene. This nonlinear mapping is the composition of several nonlinear mappings that occur in the photographic process.

Characteristic Curve [1] The exposure X is defined as the product of the irradiance E at the film and exposure time, Δt, so that its units is Jm -2. X E t After the development, scanning and digitizing processes, we obtain a digital number Z, which is a nonlinear function of the original exposure X at the pixel. Characteristic curve of the film f Z f X We make the reasonable assumption that the function f is monotonically increasing, so its inverse f -1 is well defined.

Our goal: Irradiance Reconstruction [1] Measured intensity, Z X f 1 Z Exposure, X E X t Irradiance, E

Formulization [1] The input to our algorithm is a number of digitized photographs taken from the same vantage point with different known exposure durations Δt j. We will assume that the scene is static and that this process is completed quickly enough that lighting changes can be safely ignored. It can then be assumed that the film irradiance values E i for each pixel i are constant. We will denote pixel values by Z ij where i is a spatial index over pixels and j indexes over exposure times Δt j.

Minimization Problem [1] We wish to recover the function g and the irradiances E i that best satisfy the set of equations arising from Equation 2 in a least-squared error sense. We note that recovering g only requires recovering the finite number of values that g(z) can take since the domain of Z, pixel brightness values, is finite. Letting Z min and Z max be the least and greatest pixel values (integers), N be the number of pixel locations and P be the number of photographs, we formulate the problem as one of finding the (Z max - Z min + 1) values of g(z) and the N values of lne i that minimize the following quadratic objective function: Smoothness term Minimizing is a straightforward linear least squares problem.

Minimization Problem [1] Since g(z) will typically have a steep slope near Z min and Z max, we should expect that g(z) will be less smooth and will fit the data more poorly near these extremes. To recognize this, we can introduce a weighting function w(z) to emphasize the smoothness and fitting terms toward the middle of the curve. A sensible choice of w is a simple hat function: Equation 3 now becomes:

Minimization Problem [1] Clearly, the pixel locations should be chosen so that they have a reasonably even distribution of pixel values from Z min to Z max, and so that they are spatially well distributed in the image. Furthermore, the pixels are best sampled from regions of the image with low intensity variance so that radiance can be assumed to be constant across the area of the pixel, and the effect of optical blur of the imaging system is minimized.

Construction of Radiance Map [1] Once the response curve g is recovered, it can be used to quickly convert pixel values to relative radiance values, assuming the exposure Δt j is known. For robustness, and to recover high dynamic range radiance values, we should use all the available exposures for a particular pixel to compute its radiance. For this, we reuse the weighting function in Equation 4 to give higher weight to exposures in which the pixel s value is closer to the middle of the response function:

Solution [1]

Solution [1] Z(i,j) A i+n x b k(i,j) 1) wij A(k,Z(i,j)+1)=wij w(z ij ) -wij -wij -w(z ij ) X g g(z) n=256 = wijⅹb(i,j) w(z ij +1)ⅹlnΔt j The data- fitting equations K=IⅹJ K=IⅹJ A(k,i:i+2)=lⅹw(i+1), -2ⅹlⅹw(i+1), lⅹw(i+1) for λw(z)g (z) le ln(e i ) I n+1 0 The smoothness equations n=256 I 1 1) (i,j) k: 모든 pixel 에대한일차원 index

Experimental Results [1]

Experimental Results [1]

Experimental Results [1]

HDR SHOP [2]

HDR SHOP: Download V1.0

HDR SHOP: Tutorial

HDR SHOP: Camera Curve Calibration

HDR SHOP: Camera Curve Calibration

HDR SHOP: Data

Application: Image-Based Lighting [5]

Application: Image-Based Lighting [5]

Application: Image-Based Lighting [5]

Application: Image-Based Lighting [5]

References 1. Paul E. Debevec and Jitendra Malik, Recovering High Dynamic Range Radiance Maps from Photographs, In SIGGRAPH 97, August 1997. 2. HDR shop, available at http://projects.ict.usc.edu/graphics/hdrshop/ 3. Wikipedia, High Dynamic Range Imaging, available at http://www.wikipedia.org 4. Wikipedia, High Dynamic Range, available at http://www.wikipedia.org 5. Image-Based Lighting, available at http://www.debevec.org/ibl2001/