Recently, I had the occasion to play with some features of the amazingly powerful ImageMagick image manipulation tool. After playing with several of the command-line tools and manipulations I decided to look into the API provided through the MagickWand C interface to ImageMagick. To explore some of the features available at this layer I'm attempting to develop a bleed effect on an image; similar to if you had dipped a picture in water and then hung it up to dry. I'm hoping that my free time permits and I can turn this into a small series of posts detailing how I refine this tool (if I can eventually call it that).

Perhaps in a later post I'll get into what the code looks like and a dialog of what each part does but for now I'll just put up some of the early results and learning points that I've encountered. Ultimately, I'll get the code up on github and follow along with that here.

I'm using two images for this exercise: one that contains a rainbow of colors to test and another to represent the effect on a more likely picture.

Initially, I looked at just 'dragging' each color down the image while increasing the normalization scale along the vertical to give a wash out effect further down the image. This represents how the water would continue to wash color away as it 'pulled' higher colors down the hanging image. This worked well for the rainbow version of the image:

That result has a good 'bleed' in that stronger colors last longer down the vertical. However, with the colors in the house image the washout was too aggressive and wiped out much of the original content.

If you ignore the washout, though, it is clear that the draw of colors down the image is visible (especially around the windows) meaning that reducing the washout might still produce a more realistic effect if enough of the original image could be preserved.

With that in mind, I added the ability to preserve a percentage of the original image while applying the effect. This allows a user to tune the washout per image to get just the right look. For example, too much reuse (20%) on the house and the washout effect has little impact:

But taking that down to 7.5% gets closer to what I am looking for:

There is still plenty for me to do such as handling the edges and water line better and further manipulating the washed image. For example, adding additional transforms to the result to get more seep/bleed on the washed colors. The image below shows a simple kernel convolution to add blur to the pencils, for example.

## Sunday, October 2, 2016

## Friday, May 6, 2016

### Derive formula to convert Fahrenheit to Celsius

I had been revisiting linear regression the other day and as part of that review I challenged myself to use regression to derive a well known formula without actually looking it up (the formula, that is).

The first example that came to my mind was the formula for converting temperature in Fahrenheit to Celsius. I wanted to see if I could derive that formula using two sample data sets and a simple linear regression. If the data was accurate enough, I should be able to derive the exact equation for converting between the two formats. In essence, I wanted to be able to come to the following:

Since I didn't have a data set with both types of observations available I was faced with a little 'chicken or the egg' situation. Seeing how this is just a fun little exercise I generated my own data introducing some artificial error to stand in for true observations.

After the 'observations' were available the regression was as simple as loading the data into R and running lm. I ran through the entire manual procedure of how this works in a previous post so wont repeat it here. The result of calling lm is a list and one of the elements of that list is the coefficients - these represent the intercept and slope of:

Since the Celsius observations are the response in my formula and the Fahrenheit observations are the predictors the I can create a similar equation where y represents the Celsius values and x represents the Fahrenheit values. Given that, I get the following (after plugging in the slope and intercept):

So, given observations in both Celsius and Fahrenheit (for the same events, of course) it is possible to derive an equation to convert between the two using linear regression.

My observations are very highly correlated. Obviously, as this correlation falls the accuracy of the resulting equation will suffer. Fortunately there are tools to measure the correlation which helps quantify this accuracy.

You can find the code for this exercise on github.

The first example that came to my mind was the formula for converting temperature in Fahrenheit to Celsius. I wanted to see if I could derive that formula using two sample data sets and a simple linear regression. If the data was accurate enough, I should be able to derive the exact equation for converting between the two formats. In essence, I wanted to be able to come to the following:

C = (F - 32) * 5/9

After the 'observations' were available the regression was as simple as loading the data into R and running lm. I ran through the entire manual procedure of how this works in a previous post so wont repeat it here. The result of calling lm is a list and one of the elements of that list is the coefficients - these represent the intercept and slope of:

y = mx + b

Since the Celsius observations are the response in my formula and the Fahrenheit observations are the predictors the I can create a similar equation where y represents the Celsius values and x represents the Fahrenheit values. Given that, I get the following (after plugging in the slope and intercept):

C = 0.555547 * F - 17.772318

Expanding the original equation for converting between Fahrenheit and Celsius yields:

C = (F * 5/9) - (32 * 5/9)

C = F * 0.555556 - 17.777778

My observations are very highly correlated. Obviously, as this correlation falls the accuracy of the resulting equation will suffer. Fortunately there are tools to measure the correlation which helps quantify this accuracy.

You can find the code for this exercise on github.

Labels:
fun
,
regression
,
statistics

Subscribe to:
Posts
(
Atom
)