How to find all the modes of a 3D probability distribution surface

A 3D probability distribution surface can represent the likelihood of certain events in a specific region where a higher point on the surface could mean it is more likely for the event to happen. For example, a 3D probability distribution surface created for a Wilderness Search and Rescue (WiSAR) operation, whether systematically or manually or with a hybrid, can show the searchers areas where it is more likely to find the missing person. The distribution map can be used to better allocate search resources and to generate flight paths for an Unmanned Aerial Vehicle (UAV).

An example 3D probability distribution surface

Because different path-planning algorithms may be better suited for different probability distributions (I appeal to the No-Free-Lunch theorem), identifying the type of distribution beforehand can help us decide what algorithm to use for the path-planning task. In our decision process, we particularly care about how many modes the probability distribution has. So how can we automatically identify all the modes in a 3D probability distribution surface? Here I'll describe the algorithm we used.

In our case, the 3D probability distribution surface is represented by a matrix/table where each value represents the height of the point. You can think of this distribution as a gray-scale image where the gray value of each pixel represent the height of the point. And we use a Local Hill Climbing type algorithm with 8-connected neighbors.

1. Down sample the distribution
If the distribution map is very large, it might be a good idea to down sample the distribution to improve algorithm speed. We assume the surface is noise-free. If the surface is noisy, we can also smooth it with a Gaussian filter (think image processing).

2. Check for a uniform distribution (a flat surface)
It is a good idea to check if the probability distribution is a uniform distribution. Just check to see if all values in the matrix are identical. If a uniform distribution is identified, we know the distribution has 0 mode and we are done.

3. Local Hill Climbing with Memory
Start from the a point of the surface and then check its neighbors (8-connected). As soon as a neighbor with the same or better value is found, we "climb" to that point. The process is repeated until we reach a point (hilltop) where all neighbors have smaller values. As we "climb" and check neighbors, we mark all the points we visited along the way. And when we check neighbors, we only check points we have not visited before. This way we avoid finding a mode we had found before. Once we find a "mode", we can start from another unvisited point on the surface and do another Local Hill Climbing. Here I use quotes around the word mode because we are not sure if the "mode" we found is a real mode.

4. Make sure the "mode" we found is a real mode

An Even-Height Great Wall

The "mode" we found using Local Hill Climbing might not actually be a real mode. It might be right next to a mode previously found and have a lower value (because we only checked unvisited neighbors in the previous step). It might also be part of another flat-surface mode where the mode consists of multiple points with identical values (think of a hilltop that looks like a plateau or think of a ridge). Things get even more complicated with special distributions such as this one on the right. And the "mode" point we found might be connected to a previously found mode through other points with the same value (e.g, the "mode" point is the end point of the short branch in the middle of the image.

Therefore, we need to keep track of all points leading to the final "mode" point that have identical values and check all the visited neighbors of these points, making sure this flat surface is not part of a previously found mode. If these points make up a real new mode, we mark these points with a unique mode count id (e.g, mode 3). If they are only part of a previous found mode, we mark these points so (e.g., mode 2). If one of them is right next to a previously found mode but have lower value, we mark these points as non-mode points. This step is almost like performing a Connected-Component Labeling operation in Computer Vision.

At the end of the algorithm run, we will have a count of how many modes the probability distribution has and also a map with all the mode points marked. With the Even-Height Great Wall distribution, the map would look just like the image (white pixels marking mode points) with 1 mode. And within Milli-seconds, the algorithm can identify the 4 modes in the example 3D surface above.

That's it! If you ever need to do this for your projects, you now know how!








Recursive functions work great for local hill climbing until you get a stack overflow.

AI Robot Related Conferences and Journals For My Research (Part 3)

AI Robot Related Conferences and Journals For My Research Part 2

Top Conferences
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IROS -- IEEE/RSJ International Conference on Intelligent Robots and Systems

IROS is a multi-track conference held annually. It is a premiere international conference in robotics and intelligent systems, bringing together an international community of researchers, educators and practitioners in the field to discuss the latest advancements in robotics and intelligent systems.

Every year, thousands of people all over the world attend the IROS conference and a large number of papers get published in the conference. For example, the IROS 2011 conference received 2541 papers and proposals and accepted 790 papers, with a 32% acceptance rate. However, the acceptance rate for IROS is normally much higher at around 55%. Every year the IROS has a different theme. The theme for IROS 2011 is Human-Centered Robotics, and the theme for IROS 2012 is Robotics for Quality of Life and Sustainable Development. However, people generally ignore the theme and submit whatever they have. I have been fortunate enough to attend the IROS conference in 2009 and published a paper on UAV path planning there.

The next IROS conference IROS 2011 will be held at San Francisco, California, USA.
Conference Dates: September 25-30, 2011
Submission Deadline: March 28, 2011

The next IROS conference you can submit a paper to is IROS 2012. It will be held at Vilamoura, Algarve, Portual.
Conference Dates: October 7-10, 2012
Submission Deadline: March 10, 2012



ICRA -- IEEE International Conference on Robotics and Automation

ICRA is a multi-track premiere conference in the robotics community held annually. It is in the same league with IROS and is also a major international conference with large attendance. The ICRA 2011 conference held in Shanghai, China welcomed more than 1,500 people around the world. The acceptance rate for ICRA is about 45%.

ICRA also has yearly themes. The ICRA 2011 conference's theme was "Better Robots, Better Life". The ICRA 2012 conference theme will be "Robots and Automation: Innovation for Tomorrow's Needs". Again, if you are thinking about submitting something to ICRA, don't worry about the themes. Just submit what you have on whatever topic, as long as it is related to robots or automation.

I have submitted a paper to ICRA before, but very unfortunately, the paper fell into the hands of several electrical engineer reviewers because I picked the wrong key words. They seem to hold grudges against computer science researchers. The same paper was accepted at IROS without any major revision. It is likely that I'll be submitting to ICRA again in the future, but I will be super careful about what key words to use this time!!

The next ICRA conference ICRA 2012 will be held at St. Paul, Minnesota, USA.
Conference Dates: May 14-18, 2012
Submission Deadline: September 16, 2011

AI Robot Related Conferences and Journals For My Research Part 4


Video of the Day:

This is why the back of my jersey has Messi's name on it!

Robot of the Day: MABEL, the Two-Legged Running Robot

MABEL (not an acronym) is the name of a bipedal "humanoid" robot created by researchers at University of Michigan. It just got its fame recently because it could run in a human-like gait at speeds up to 3.06 meters/second. That is 6.8 miles per hour. That is the world record for a bipedal robot with knees.

MABEL was originally built in collaboration with Jonathan Hurst, then a doctor student at the Robotics Institute at Carnegie Mellon University. Then researchers at U-M spent years improving the feed-back system in MABEL's training. MABEL was intentionally built to look like a human, with a heavier torso and light flexible legs. When it is running, MABEL is in the air for 40 percent of each stride, which is almost like a real runner. The robot can self balance in real time with a closed-loop control, and switch gaits as commanded autonomously. It can even transition from completely flat surface to uneven grounds. The video below shows MABEL running.

The researchers envision that two-legged robots can travel over rough terrains and function better in places built for humans. They can be used to enable wheelchair-bound people to walk again or to be used for robot rescuers that can step over small obstacles. Biped robots certainly have the advantage over wheeled robots when it comes to bumpy surface or stairs, however one important factor is that biped robots look more human-like compared to say a three-legged or 6-legged robot. The truth is that many four-legged animals run much faster than us two-legged human, and multiple-legged insects handle uneven surface much better than two legged ones. But would you rather have a two-legged humanoid robot serving you a drink or an eight-legged spider-looking one? Actually even the same MABEL robot walking backward looks more like a bird and seems weird (see video below).

I could envision multiple-legged robots to be very useful in space colonization. Most likely the surface terrain at another planet would not be flat, and the multiple-legged robots could easily transport goods for human and explore the planet surface more efficiently.

Back to the MABEL robot. It's hard to describe the feeling when I watched the robot running with large strides. There's certainly some uncanny valley effects there, but there's something beautiful about the strides, because they looked natural. Now we just have to put a soccer ball in front of it and then teach it to dribble and shoot...

To find out more about the MABEL robot, visit the researcher's project page here.


Video of the Day:

An interesting Logitech commercial showing a biped humanoid blending in the human environment. Enjoy!

AI Robot Related Conferences and Journals For My Research (Part 2)

AI Robot Related Conferences and Journals For My Research Part 1

Top Conferences
==================================================================

HRI -- ACM/IEEE International Conference on Human-Robot Interaction

HRI is a single-track, highly selective annual international conference that seeks to showcase the very best interdisciplinary and multidisciplinary research in human-robot interaction with roots in social psychology, cognitive science, HCI, human factors, artificial intelligence, robotics, organizational behavior, anthropology and many more. HRI is a relatively new and small conference because the HRI field is relatively new. The 1st HRI conference was actually held here in Salt Lake City, Utah, in March 2006, and my advisor, Dr. Michael A. Goodrich, was the General Chair for the conference. It is very unfortunate that I only started grad school two months after the 1st HRI conference and missed this great opportunity. *Sigh* HRI has been growing rapidly and gaining attentions from many research groups and institutions. The last HRI conference (6th) had attendance exceeding 300 participants. HRI is also a top-tier conference with an acceptance rate between 19% and 25%. As the conference becomes more and more popular, researchers from many research disciplines (e.g., human factors, cognitive science, psychology, linguistics, etc.) began participating in the conference.

The venue of the HRI conference rotates among North America, Europe, and Asia. I have been lucky enough to attend the conference twice, once in 2010 and once in 2011. In 2010, I attended the HRI Young Pioneer Workshop. The workshop is a great event because you not only get to make friends with a bunch of young researchers in the HRI field before the conference starts, you also get to see what other young researchers are working on. Besides, NSF is generous enough to cover a good portion of the airfare, which is great help for poor grad students. I liked the workshop so much that I joined the organizing committee for the next year's HRI Young Pioneer Workshop, and also hosted the panel discussion at the workshop. That was also the reason why I was able to attend HRI 2011. Also in both HRI 2010 and HRI 2011, I guarded my advisor's late-breaking report poster sessions because he couldn't make it.

I have never submitted anything to the main HRI conference. Since this is the top conference in my research field, I'd like to publish something before I graduate.

The next HRI conference HRI 2012 (the 7th) will be held at Boston, Massachusetts, USA.
Conference Dates: March 5-8, 2012
Submission Deadline: September 9, 2011



CHI -- ACM/SIGCHI Human Factors in Computing Systems - the CHI Conference

CHI is considered the most prestigious conference in the field of human-computer interaction.It is a multi-track conference held annually. Because of the heavy interests and involvement from industry leaders, large tech companies such as Microsoft, Google, and Apple are frequent participants and organizers of the conference. CHI is a top-tier conference with acceptance rate between 20% and 25%.

Human-Computer Interaction is a broad field that includes both software and hardware. The goal of HCI is to develop methods, interfaces, interaction techniques to make computer devices more usable and receptive to the user's needs. These days computer devices could include a wide variety of things such as cell phones, tablets, game consoles, or gadgets. Thanks to the advancement of sensor technologies, a whole set of rich interaction techniques have emerged to work with gestures, device orientations, and motion of the device.

Many of the HCI design principles, interface designs, and interaction techniques are relevant in Human-Robot Interaction. After all, a robot must have some kind of computer embedded (whether tiny or full-size, whether one or multiple). In many HRI tasks, the human user could very well be interacting with the robot through a regular computer or a touch screen device (think tele-presence, for example). I have never attended the CHI conference before, but I have heard a lot about it from Dr. Dan Olsen at BYU because he was always some kind of chair in the CHI organizing committee. In fact, he'll be the paper chair in the next CHI conference.

The next CHI conference CHI 2012 will be held at Austin, Texas, USA.
Conference Dates: May 5-10, 2012
Submission Deadline: September 23, 2011

AI Robot Related Conferences and Journals For My Research Part 3





Every time when you clip your finger nails, think what you have achieved since you last clipped your finger nail. If you can remember what you did, then you have not wasted your life.

Seven Weapons - Longevity Sword: Chapter 1 (3)

THREE

Miao Shaotian walked at the very end, gripping the pair of golden rings tightly in his hands, so tight that the blue veins on the back of his hands almost popped out.

He shouldn’t have come, but he must.

That merchandise seemed to be emitting a strange field of attraction, sucking him close one step after another. He was not going to give it up until the last moment.

Two statue-like guards stood at the entrance of the underground tunnel. Then for every dozen steps forward, two more guards stood along the way, their faces as grim as the green stones in the walls.

A rampant green dragon was carved onto the stone walls.

It was said that the Green Dragon Clan had three hundred and sixty-five secret branches. This was undoubtedly one of them.

At the end of the underground tunnel stood a gate made of very thick iron railings.

Gongsun Jing took out a large chain of keys from his waist band and then opened three locks with three of them. Only then did the two guards behind the iron bars pulled the gate open.

But this was still not the last gate.

“I know many people can get in here. The guards here are not difficult to deal with. But from here onward would prove to be an arduous task,” Gongsun Jing explained.

“Why’s that?” Young Master Zhu asked.

“Between here and that stone door over there, there are a total of thirteen hidden traps. I can guarantee that there are no more than seven people in the entire world who could successfully get through all thirteen traps.”

“Luckily I am definitely not one of those seven people,” Young Master Zhu heaved a sigh.

“Why don’t you give it a try?” Gongsun Jing smiled even more politely.

“Perhaps I’ll give it a try at a later time, but not right now,” Young Master Zhu said.

“Why not now?” asked Gongsun Jing.

“Because I am perfectly happy staying alive,” replied Young Master Zhu.

The distance between the iron bars and the stone door was actually not far, but after hearing Gongsun Jing’s words, the path seemed to be ten times farther, and the stone door seemed to be even heavier.

Gongsun Jing used another three keys to unlock the door.

Behind the two-foot thick stone door was a nine-foot wide stone cell.

The room was ghastly and chilly as if it were the center of an ancient emperor’s tomb, only that a giant iron chest sat at the spot instead of the coffin.

Opening the iron chest of course required another three keys, but that was not the end of it because there was a small iron chest inside the giant one.

“Such maximum security perhaps deserves some higher prices from us,” Young Master Zhu said with a sigh.

“Young Master Zhu is very clever indeed,” said Gongsun Jing with a big smile.

Taking out the small iron chest, he unlocked it and opened the lid, but all of a sudden, his affable smile disappeared and his face looked as if someone had just shoved a rotten tomato down his throat.

The small iron chest turned out to be empty except a single piece of paper.

The paper only showed nine words, “Thank you! You are such a nice guy!”

Now support the translator Lanny by following my blog and leaving comments! :)

Video of the Day:

Excerpt from the Shanghai World Expo Closing Ceremony Concert - Fusion of Art and Music. Enjoy!