Daniel Moreno (damoreno)

Once the radiance map was recovered, we like to map the world radiance values to a small range suitable for visualization. First, I have tried the global operator from Reinhard al. et al. 2002 but later I decided to implement the modified version presented in Drago et al. 2003 "Adaptive Logarithmic Mapping For Displaying High Contrast Scenes" because it includes a parameter b that can be adjusted according to the desired brightness in the final image. Additionally, the paper proposes a modified version of the gamma function which I have applied to my images in order to replicate their results.

The equation of this operator is the following:

As local tone mapping scheme I have implemented the simplified version of the method proposed Durand 2002 as detailed in the project handout. The key idea is to split the image in three layers, base, detail, and color, and to process  each one differently: base intensity is compressed to match the display values, details are added to keep scene fidelity, and colors are applied unmodified.

I have implemented the Fast Bilateral Filter as described in Sylvain Paris presentation as extra credit. A simple implementation of a bilateral filter is very slow because, different from a Gaussian blur, it cannot be represented as a separable kernel and applied as separate convolutions in rows and columns. To solve this issue, Fast Bilateral Filter extends the domain to one extra dimension containing the range values (e.g. in the case of images the domain is extended to a 3D volume with x, y, and intensity as axis). In this extended domain, the filter can be expressed as a separable kernel and applied to each axes independently as other linear filters. Once the volume has been processed, the final step is to extract the filtered intensity values from it and build a filtered image. To reduced the size of the extended representation in memory and speed-up the convolution, the original domain is upsampled by some factor. The final values are recovered by trilinear interpolation.

It is known that for-loops are specially slow in Matlab and I have done no special optimization to minimize loops usage in any of my two filter implementations. For instance, the standard filter implementation requires four nested loops in order to traverse all the image pixels and compute the two-dimensional convolution. In the case of the Fast Filter implementation my code includes several more loops: two nested loops to traverse the image and build the volume, three-nested loops to traverse the volume, the volume is traversed three times (one for each axes convolution), and two extra nested loops to extract the final values from the filtered volume and build the output image.  However, as can be seen in the table below, the Fast Bilateral Filter implementation took less than a minute to filter the test image, whereas the standard implementation ran for six minutes. The improvement is about 6X besides the non-optimal implementation.

In all my tests I have used a down-sampling factor of 4 in the spatial coordinates and I have divided the range values in  10 bins.
 

	Standard Bilateral filter	Fast bilateral filter
Execution time for "garage" test image	359.62 seconds	56.47 seconds

From the result images above is clear that the linear mapping is not enough to represent the scene radiance in the compressed image format, and that the other two methods deliver acceptable results. The only observation I like to make about them is that neither is better than the other for all scenes. For instance, the "arch" on top have ghosts in the local tone mapping meanwhile the other version looks great. Similarly, the "window" image colors look unreal in the right image. On the other hand, the outdoor images look washed-out in the global operator column but the local tone mapped ones look very good. Finally, I have not played with all the available parameters in both methods, I just have chosen values that worked fine in general and used them for all the images. Thus, these results are not the "best ones" but are representative for the general case.