The final project was to combine a path traced object with a real photograph—creating a “special effects” style image. I thought this was quite successful. The winning image was created by Zhan Fam Quek:

This was created using a path tracer written by the students, using a HDR environment map and HDR background image captured by the students.

More images from the final project can be found in the course gallery. Slides and assignments can be found on the course webpage.

To address this problem some automatic text layout systems rely on dictionaries in which acceptable hyphenation points have been marked by a human. While generally correct, such dictionary-based approaches require a very large data file to store the dictionary and fail when given new words. An alternate approach, taken in TeX, is to summarize hyphenation points into a small set of patterns which can then be applied to any word. The TeX method was described in Franklin Liang’s thesis Word Hy-phen-a-tion by Com-put-er. Liang’s thesis claims that his pattern-based finds about 90% of the human marked hyphenation points and finds essentially no incorrect ones.

Unfortunately, essentially no incorrect ones is not the same as no incorrect ones. In the last two papers I’ve written, I’ve come across words that TeX’s method failed rather dramatically on. Fortunately, LaTeX provides an easy way to override the automatic hyphen selection through the \hyphenation{} command.

\hyphenation{white-space} fixes TeX’s “whites-pace”, a somewhat racist rendering. Note that this incorrect hyphenation is the opposite of the “new-spaper” example, which came from Liang’s thesis, highlighting the problems facing a purely pattern-based approach.

\hyphenation{analy-sis} fixes TeX’s “anal-ysis” which leads to a rather infelicitous mispronunciation of the first part of the word.

Despite doing a good job most of the time, TeX’s automatic hyphenation can and does go awry. Keep your eyes open when proof reading!

*I’m pretty sure TeX gets the hyphenation of “mistakes” correct.

In standard importance sampling you have to draw samples from a distribution which can be sampled and which has a known scaling factor (so that the area under the pdf = 1). This is very limiting in some MC situations, such as sampling the incoming light direction in a path tracer. The function we want to sample from is the product of the BRDF and the incident light field. However, we can typically only sample from one component or the other, not both. In RIS, we create a sampled, discrete approximation to the desired distribution and then draw our samples from that. Since the approximation is discrete we can easily normalize it and draw samples from it. In my thesis, I showed that when weighted correctly, this results in an unbiased estimate.

RIS will beat IS when it is substantially cheaper to create the approximate distribution than it is to evaluate the true function. In the path tracing context, I did this by evaluating the BRDF and environment map lighting for the approximate distribution, but not the visibility (the ray tracing step). With this approach, the RIS image (on the right) has substantially lower variance than the IS image (left).

As long as the visibility test accounts for a substantial fraction of the execution time, RIS will beat IS. However, this wasn’t particularly true when I wrote the thesis and is probably less true now. In my thesis, I concluded that, for current rendering tasks, RIS wasn’t a big win since the difference in evaluation cost between the approximate samples and the actual samples wasn’t very high. However, I think it could be quite useful in some MC applications where a relatively good and cheap discrete approximation can be found.

We frame the aspect ratio selection problem as one of minimizing the length of the data curve while keeping the area of the plot constant. This leads to a method that is substantially more robust than previous approaches. We’re also able to demonstrate empirically that the resulting aspect ratios are a compromise between those suggested by previous methods. As shown below, the arc length method can also effectively bank both standard line charts (in this case a loess regression line) as wells as contour charts.

Perhaps the most surprising result is that good aspect ratios can be selected without explicit reference to the slopes or orientations of the line segments within the plot.

Let me know if you run into any problems with it or have any suggestions for improvement.

A few small bugs in the implementation of our algorithm have been fixed thanks to feedback from Ahmet Karahan who is working on a Java version. I have also added a number of other labeling algorithms that have been proposed or used in the past, including those by Sparks, Thayer, and Nelder (from about 40 years ago), and adaptations of the matplotlib, gnuplot, and R’s pretty labeling functions.

Hop visual interface

The graphical elements were produced using Protovis since I needed an excuse to play around with it. We ran into minor performance problems using Protovis for so many plots in a single page. In a production system it would be wiser to generate and cache the plots on the server side.

Update: The screenshot shows a task scheduling imbalance bug that we found in HOP using the visual interface.

The abstract:

The non-data components of a visualization, such as axes and legends, can often be just as important as the data itself. They provide contextual information essential to interpreting the data. In this paper, we describe an automated system for choosing positions and labels for axis tick marks. Our system extends Wilkinson’s optimization-based labeling approach to create a more robust, full-featured axis labeler. We define an expanded space of axis labelings by automatically generating additional nice numbers as needed and by permitting the extreme labels to occur inside the data range. These changes provide flexibility in problematic cases, without degrading quality elsewhere. We also propose an additional optimization criterion, legibility, which allows us to simultaneously optimize over label formatting, font size, and orientation. To solve this revised optimization problem, we describe the optimization function and an efficient search algorithm. Finally, we compare our method to previous work using both quantitative and qualitative metrics. This paper is a good example of how ideas from automated graphic design can be applied to information visualization.

Update: We’ve released a preliminary R package implementing the three labeling algorithms we compared in the paper. Feedback is appreciated. The final version should be released by InfoVis (in October).