High Dynamic Range Imaging

• Given a series of photographs for a scene under different exposures, output an HDR image and, optionally, the response curve of the camera.
• With the responsive function, we can reconstruct the radinace map and output it as a Radiance RGBE image (.hdr)
• Finally, tone map the radiance map (HDR) to a low dynamic range (LDR) image.

Usage

Data Preparation (Optional)

• Place your images of different exposure times under $INDIR

• Run the following command, which will automatically read the exposure times of images under $INDIR and create exposure_times.csv

  python3 read_exposure.py $INDIR
  # E.g., 
  # python3 read_exposure.py ./data/team26_2

Running the Code

• Command

  python main.py [--indir $INDIR] [--outdir $OUTDIR] [-d $DEPTH] 
  [-w $WEIGHTING_FUNCTION] [--lamb $LAMBDA] [--alpha $ALPHA] 
  [--gamma $GAMMA] [--tm $TONEMAPPING_METHOD] 
  
  # E.g.,
  # python3 main.py --indir ./data/team26_2 --outdir ./data

1. Image Alignment (MTB Algorithm)

• Align all images before further processing.

  	w/o alignment	w/ alignment (d=10)
  team26_2

2. HDR Reconstruction (Debevec's Method):

• Reference : Recovering high dynamic range radiance maps from photographs
• Combine the aligned images to recover the scene's radiance map.
  • By rewriting the objective $O$ into the form of $Ax=b$, we can solve $x = [g(0) \dots g(255) \ lnE_1 \dots lnE_n]^T$, getting $g$ such that $g(Z_{ij}) = ln(X_{ij})$ $$O = \sum_{i=1}^{N} \sum_{j=1}^{P} {w(Z_{ij}) [g(Z_{ij}) - ln E_i - ln \Delta t_j]}^2 + \lambda \sum_{z=Zmin+1}^{Zmax-1} [w(z)g''(z)]^2 $$
• Recover HDR Radiance map by Camera Response Function
  • With $g$, we can compute the radiance of each pixel $i$ based on $$E_i = e^{\frac{{\Sigma_{j=1}^{P}{w(Z_{ij})(g(Z_{ij}) - ln \Delta t_j)}}}{\Sigma_{j=1}^{P}w(Z_{ij})}} $$

3. Tone Mapping

• Reference : Photographic Tone Reproduction for Digital Images

• Global and Local operators (dodging and burning) are implemented to converts the HDR image into a LDR image suitable for displaying on standard monitors.

• Global Method $$\overline L_w=e^{[\frac1N \Sigma_{x,y}log(\delta + L_w(x, y))]}$$ $$L_m(x, y) = \frac{\alpha}{\overline L_w}L_w(x, y)$$ $$\rightarrow L_d(x, y) = \frac{L_m(x, y)(1+\frac{L_m(x, y)}{{L_{white}(x, y)}^2})}{1+L_m(x, y)}$$

• Local Method $$V_i^{blur}(x, y, s) = L_m(x, y) \otimes G_s(x, y, s)$$ $$V_s(x, y, s) = \frac{V_1^{blur}(x, y, s) - V_{2}^{blur}(x, y, s)}{2^{\phi} \frac{\alpha}{s^2}+V_1^{blur}}, s_{max} \ni |V_{s_{max}}(x, y) < \epsilon|$$ $$\rightarrow L_d(x, y)=\frac{L_m(x, y)}{1+V_1^{blur} \left( x, y, s_{max}(x, y) \right)}$$

• Comparisons of global and local methods

  	Global	Local
  testcase_1
  testcase_2