High dynamic range imaging by multiple exposure image.

Create a single high dynamic range image from multiple exposure bracketed images fusion. I have completed this term project for DIP course.

I have assigned two processes for this project.

Process I :

Input Images:For this project, we have considered 16 input images of dimension 768*512*3 taken with different exposures.

The exposure times for the 16 images are as follows [30; 15; 8; 4; 2; 1; 1/2; 1/4; 1/8; 1/15; 1/30; 1/60; 1/120; 1/250; 1/500; 1/1000].

The process will be discussed in the following steps:

Step 1: First, we have to recover radiometric response curve. For that purpose I have used some mathematical equations which are taken from this paper and they are as follows:

where, P is the number of images, N is the number of pixels in images, z(i,j) is the pixel values of pixel location number i in image j, w(z) is the weighting function value for pixel value z and . Also, for

= , otherwise.

The w(z) is used for enhance the smoothness. Now, given z, log shutter speed, λ= 1 and weight, we get the image system's response function g and hence the response curve.

Step 2: Radiance Map Reconstruction

The radiance map can be computed using the recovered response obtained from tln(radiance at the ith pixel) = g(ith pixel value in image j) - ln(exposure time of image j). Mathematically, .

Step 3: Tonemapping

I have employed linear normalisation technique to achieve the required tonemapping.

tonemapped image = (img — img.min()/img.max() — img.min()).

Step 4: Gamma correction

gammaCorrectedImage(x,y) = .

If we increase the value of γ, the image becomes darker; whereas, the image becomes brighter for decreasing values of γ. For my analysis, γ= 1.5 produces good results.

Step 5: Visualizing HDR images

The final HDR image can be visualized from the gamma correction response by using the inbuilt Matlab functions 'hdrwrite' , 'hdrread' and 'imshow'.

Output:

Code: HighDynamicRange.m

References :

1. https://towardsdatascience.com/hdr-imaging-what-is-an-hdr-image-anyway-bdf05985492c
2. Debevec, P. E., & Malik, J. (2008). Recovering high dynamic range radiance maps from photographs. In ACM SIGGRAPH 2008 classes (pp. 1-10).

Process II:

Input : Image1, Imag2, Image3. Image3 have the high pixel values and Image2 have the less pixel values.

Steps:

1. match1 = imhistmatch(Image3, Image2);

2. match2 = imhistmatch(match1, Image1);

3. Use median filter on match2 and convert to HDR image.

4. Apply inbuilt matlab function tonemap on HDR image.

Output:

Histograms :

Code: hdr1.m