Creating HDR image from image stack with multiple exposures

The goal of this project is to recover high dynamic range radiance maps from photographs to crease an image that captures details from the entire dynaimic range. This project has two parts, radiane map construction and tone mapping. For the first part, we implement algorithm from Debevec, Malik to recover high dynamic range radiance map. Then we apply tone mapping and intensity adjustmemt to to convert the radiance map into displayable image.

1. Film Response Curve Recovery

Film response curve is a function maps from observed pixel values on an image to the log of exposure values: g(Zij) = ln(Ei) + ln(tj). To recover function g, we implement equation from Debevec

g is the unknown response function

w is a linear weighting function. g will be less smooth and will fit the data more poorly near extremes (Z=0 or Z=255). Debevec introduces a weighting function to enphasize the smoothness fitting terms toward the middle of the curve.

t is the exposure time

E is the unknown radiance

Z: is the observed pixel value

i is the pixel location index.

j is the exposure index

P is the total number of exposures.

This response curve can be used to determine radiance values in any images acquired by the imaging processing associated with g, not just the images used to recover the response curve.

2. High Dynamic Range Radiance Map Construction

Once the response curve g is recovered, we can construct a radiance map based on equation from Debevec

In order to reducing noise in the recovered radiance value, we use all the available exposrues for a particular pixel to computer its radiance based on equation 6 in Debevec.

Global tone mapping: In this project, we use gamma correction as global tone mapping. The output image is proportional to the input raised to the power of the inverse of gamma and has pixel value range from 0 to 255.

In order to construct HDR image to be as closer to input image as possible, we adjust the output image average intensity for each channel (B, G, R) to be the same as template image. In general, we use middle image from image stack as template, which is usually most representative of the ground truth.

Exposure 1/160 sec	Exposure 1/125 sec	Exposure 1/80 sec	Exposure 1/60 sec	Exposure 1/40 sec	Exposure 1/15 sec

Exposure 1/400 sec	Exposure 1/250 sec	Exposure 1/100 sec	Exposure 1/40 sec	Exposure 1/25 sec	Exposure 1/8 sec	Exposure 1/3 sec