## New FloatImage Class Methods and Gamma

First, grab the new basecode from Canvas. Among other additions, the FloatImage class now includes some additional operators that allow you to add, subtract, multiply and divide images element-wise. For example:

FloatImage im1(640,480,3), im2(640,480,3);
float a = 2.0, b = -1.0, c = 0.0;
FloatImage out1 = im1 + im2;
FloatImage out2 = im1 - b;
FloatImage out3 = a * im2;
Image out3 = im1/c; //this will throw a DivideByZeroException()

As you can see, these operators can be used the same way as any built-in type like float. For more information, please read floatimage.cpp.

### Gamma

Typically, 8-bit images are gamma-encoded. Meaning, to reduce the effect of quantization on the darker tones, the scene's radiance $$x$$ is not stored, but $$x^\gamma$$ is stored instead (where $$\gamma \approx \text{1/2.2}$$).

## Colorspaces

In this section, you will implement several functions related to changing an image from RGB colorspace to other colorspaces.

### Luminance-Chrominance

When we convert a color image to grayscale using the color2gray function, we get the luminance of the image, but lose the color information or chrominance (kr,kg,kb). You can compute this chrominance by dividing the input image by the luminance. Once the luminance and color information have been separated, you can modify them separately to produce interesting effects.

### YUV

Another representation of an image that separates overall brightness and color is the YUV colorspace. An RGB image can be converted to and from a YUV image using the matrix multiplications $\left[ \begin{array}{c} Y\\ U\\ V \end{array} \right]= \left[ \begin{array}{ccc} 0.299 & 0.587 & 0.114 \\ −0.147 & −0.289 & 0.436 \\ 0.615 & −0.515 & −0.100 \\ \end{array} \right] \left[ \begin{array}{c} R\\ G\\ B \end{array} \right], \\ \left[ \begin{array}{c} R\\ G\\ B \end{array} \right] = \left[ \begin{array}{ccc} 1 & 0 & 1.14 \\ 1 & -0.395 & -0.581 \\ 1 & 2.032 & 0 \end{array} \right] \left[ \begin{array}{c} Y\\ U\\ V \end{array} \right].$

### Discussion

The chrominance-luminance and the YUV conversions perform similar operations: they decouple an images intensity from its color. There are, however, important differences. YUV is obtained by a purely linear transformation, whereas our chrominance-luminance decomposition requires a division. Furthermore, the latter is overcomplete (we now need 4 numbers), while YUV only requires 3. YUV does a better job of organizing color along opponents and the notion of a negative is more perceptually meaningful. On the other hand, the separation between intensity and color is not as good as with the ratio computation used for luminance-chrominance. As a result, modifying Y without updating U and V changes not only the luminance but also the apparent saturation of the color. In contrast, because the luminance-chrominance decomposition relies on ratios, it preserves colors better when luminance is modified. This is because the human visual system tends to be sensitive to ratios of color channels, and it discounts constant multiplicative factors. The color elicited by r, g, b, is the same as the color impression due to kr, kg, kb, only the brightness/luminance is changed. This makes sense because we want objects to appear to have the same color regardless of the amount of light that falls upon them.

## Spanish Castle Illusion

You can use the colorspace functions you implemented to implement the Spanish castle illusion, which you can read more about here.

Given an input image, you should create two images. The first image has a constant luminance (Y) and negative chrominance (U and V), and the second image is a black-and-white version of the original, i.e. both U and V should be zero. In the first image, set the luminance to be 0.5. To help people focus on the same location, add a black dot in the middle of both images. If image has dimensions $$w \times h$$, make sure that the black dot is at the 0-indexed location floor(w/2), floor(h/2).

You can try out the Spanish castle illusion using the images castle_small.png and wheat.png provided in the Input directory located in this assignment's skeleton code.

## White balance

You will implement a function to automatically white balance an image using the gray world assumption, in which the mean color of a scene is assumed to be gray. You do this by multiplying each image channel with a factor. The goal is to make the mean of each of the three channels in the output image the same.

You can try out white balance using the image flower.png provided with your skeleton code.

## Histogram

In this part of the assignment you will implement functionality to visualize and manipulate image histograms.

## Submission

Turn in your files using Canvas and make sure all your files are in the a2 directory under the root of the zip file. Include all sources (.cpp and .h) files, any required input, and the output of your program. Don't include your actual executable (we don't need your _build directory), and remove any superfluous files before submission.