Moiré Patterns

Moiré pattern

Some time ago I reblogged a post from El Ojo Inoportuno showing Moiré pattern, which resulted from taking a photo of a circular pattern of (beautiful) tiles. This phenomenon is caused by undersampling and is also called space aliasing. There’s a very good explanation of space aliasing and another stunning Moiré example on Agile Geoscience’s post N is for Nyquist.

Creating Moiré patterns

One way to get Moiré pattern is to superimpose two identical, transparent line gratings and rotate one by an angle. You can see an animation of this on Wolfram Mathworld here; notice that the pattern varies with the angle. In the same page there’s also an example of Moiré Patterns generated by plotting series of curves on a computer screen, which is very similar to taking the photo of circular tiles shown in the Ojo Inoportuno photo. Again the interference is caused by representing circles with a finite size pixel grid. If you are interested you can experiment with these effects and many more by downloading templates from this site. Figure 1 shows my own Moiré from circular patterns.


Figure 1


There is a program for interactive Moiré pattern experiments called iMoiré.

Another way to get a Moiré pattern is to scan a picture printed with halftone. There’s a simple explanation of this scanning-generated interference here. Again this is a matter of aliasing, or undersampling. Here’s a good example:

Figure 2

The original image is a lovely watercolor by  Ettore Roesler Franz showing medieval houses along the Tiber river in Rome. The Moiré Pattern results from scanning the watercolor from one of the book collections (the image was posted on Flickr here).

How to remove Moiré pattern from digital images

For a quick solution, there’s a good article with detailed instructions on how to remove Moiré pattern in Photoshop, Paint Shop Pro, etcetera. For a more advanced workflow there’s an excellent top hat filter in Photoshop included in Reindeer Graphic’s FoveaPro plugin. In Figure 3, I created a sort of pictorial chart of this workflow using low resolution copies of examples in The Image Processing Cookbook, by John C. Russ.


Figure 3


In future posts I plan to show how to remove Moire’ pattern with open source code images  using Python, and then to extend the workflow to the removal (or attenuation) of acquisition footprint in seismic data, which has a very similar appearance in the 2D Fourier domain, and can be filtered with very similar techniques.



Some photos of Northern British Columbia wildlife and geology


Last week I went  on a helicopter ride with Gerry, my father in-law, to count of Kokanee Salmon in the  Camp Creek near Valemount, BC. We were invited by Curtis Culp of Dunster, BC, which is in charge of this  conservation effort run by BC Hydro. Here’s a picture of Gerry leaving the chopper (from Yellowhead Helicopters).


Kokanee salmon is a land-locked relative of Sockeye salmon. This means that they spend all their life in inland lakes, never seeing the ocean. For spawning  they enter inlet streams of the lake where they live. Camp Creek is a smaller tributary of the Canoe River, inlet of the Kinbasket Lake, where these Kokanee live.

The number of fish is estimated visually from the helicopter using a hand-held tally counter (every ~100-fish patch is a click). As a matter of facts, Curtis and Gerry counted fish, and I went along for the fun. Their estimates were really close, coming in at 15,000 and 15,400 in ~35 minutes over a ~15 km stretch of the Camp Creek. I counted 15 between Bald eagle and Golden eagle, and took some photos. Here they are!

Wildlife and nature photos

The first two are photos looking straight down the Camp Creek. Believe it or not, there’s fish there. See the dark spots? Those are Kokanee Salmon. And the job was to count them, so I am glad I did not have to (although it was easier to the naked eye).



The next two are a couple of photos taken at the ground level, courtesy of Curtis. Here the salmon is easy to see.

Kokanee ground

Kokanee ground1

The next two are also photos of the creek from the helicopter. There’s fish in there but I can only say it because I saw them, I can’t quite make them up in the photos. I love the shots though, the crystal clear water and the shadows.



The following two are photos with eagles. I could not believe how tiny they look, since even at this distance they seemed huge to the naked eye. There is a bald eagle in the first photo (middle left) , the other two (in the middle of the second photo) are too tiny, it is hard to say.



This last one is a photo of the trees, just looking down. I find it mesmerizing.trees

Upon looking at all the photos (I took about 80) I have to say that as much as I love my iPhone 4S, they are not nearly as good as I had wished for. Certainly far from the photos I shot during a claim staking trip in the Cassiar Mountains near Watson Lake, Yukon using a Canon FTb 35 mm (one of these days I’ll have to get those photos out of the attic and publish some of them). I often think of going back to my reflex camera, although I hear the iPhone 5 camera is a big improvement, with the iPhone 5S being even faster, so there’s hope.

Bonus photo

Here’s a beautiful elk. I took it another day, on the highway just outside of Jasper, but I thought it would fit in here.


Geology photos

I love meander rivers so I took a whole lot of photos of the creek. The first one shows a nice sandbar right where we started the counting.


This next one is a nice shot of the meandering creek looking back.

Camp Creek

In this third one you can see two nicely developed meander loops with point bars.


Last, but not least, a really tight meander. I love this photo, it’s my overall favourite.


Human activity photos

I am also including some photos showing the human footprint on the land. This first one is a clearing – I am not certain for what purpose, likely a new development. The circular patches are places where the logs were collected and burned. Quite the footprint, seen from here.


Next is something I did not expect to see here, a golf course – although I probably should have…. they are omnipresent, and often obnoxious, to say the least.


This is one I quite like: the creek, the railway, and the Yellowhead highway, all running next to one another.


The team

Finally, a shot of Gerry and I in the back of the chopper and one of Gerry counting.



Beautiful Geology from space

In my post Our Earth truly is art I talked about Earth as Art, NASA’s  e-book collection of wonderful satellite images of our planet, and posted my top 3 picks.

In NASA’s Perpetual Ocean animation I talk about a beautiful convergence of maps and art: The Turbulence of Van Gogh and the Labrador Shelf Current, and NASA’s Perpetual Ocean animation.

Here’s another gem: Van Gogh from Space Landsat 7 Acquired 7/13/2005, winner of NASA’s public contest to select the Top Five ‘Earth as Art’ Winners


Geology photo quiz #1

Take a look at the photo below, which I took it on the way up to McBride Peak (in McBride, British Columbia). It is a view up the Sunbeam Creek, part of an Ecological Reserve. Question: why would (only) part of the creek be so white? My father-in-law and I had been wondering since a previous hike to the top of the Peak, and speculations were running rampant. Finally, yesterday, we decided to hike up to the top again, then go down to the creek to find out. I think we did, and it was a great hike and a lot of fun. I am in the process of writing a nice post on this geo-adventure, but I though in the meantime I’d post the photo and make it a quiz.


I will give readers two clues:

1) the mysterious white “stuff” sits in a creek where water is actually running;

2) this is a south face, exposed to the sun all day long, so it couldn’t be snow or ice.

Below is a close-up photo. So, what do you think it is?
Or at least, what do you think it could be?



I love this photo (thanks to Carlos Mario del Rio for posting it)!
There’s something about tiled floors (and tiles in general) that has always mesmerized me and this is a really good one. I like the unusual perspective too.
There’s a radial pattern and a circular pattern of tiles, but if I stare at the photo I also see hints of an interference pattern, an intriguing flower pattern. I think this is a genuine Moiré pattern, one quite well known to photographers, generated by interference between circles of varying distance with the camera’s sensor pixel grid.
In my next post I will look in more detail at Moiré patterns and try to explain how they form.
I will show how the effect can be removed, or at least reduced, particularly from scanned images. Similar techniques can be used to remove acquisition footprint from reflection seismic data, which will be the topic of an upcoming series on MyCarta.

Our Earth truly is art

NASA has published a number of really good e-books on planetary science. Typically, each time I stumbled on one, I added a link on my Books page, but I could not skip writing about the latest one, which I discovered thanks to this post on FlowingData. It’s called Earth as Art, and it’s a fantastic book!

The pictures in this book are truly marvellous, and a thing of art. Here are my three favourites – I am so mesmerised by them I can’t stop looking (particularly the Ugab River one).

Enjoy. Check the book, and let me know which ones you like.


Von Kármán Vortices, Southern Pacific Ocean


Ugab River, Namibia


Shoemaker Crater, Australia

Google Earth and a 5 minutes book review: Geology Illustrated

A few years ago I bought on e-bay Geology Illustrated – by John S. Shelton, for just 10 US dollars. Every time I look at, and inside the book I can’t but think those were the best 10 dollars I ever invested in books.

There are already reviews and plenty of praise for this book out there – no need to repeat any of that if not briefly. My take is that the geology is clear and well explained. A bit simple, but simple is not always bad. And Shelton himself in the preface recommends this book as a “point of departure rather than something to lean on…” but that is perfect if you are a teacher looking for material, a first year college student, or a non-geologist looking for a high quality introduction.

But the photographs are priceless, and Shelton, who was also a pilot, took them all himself. Again, the author reminds us that nothing can replace field experience, and having  been trained as a field geologist (an average one, but that’s another story) I cannot but agree. However, lacking access or time to go to the field, or both, I find looking at a book like this can be an extraordinary substitute. That is especially true if you combine the reading with using Google Earth (particularly if you are a visual-spatial learner) and that is exactly what I did.

I already praised Google Earth for visualisation in this post. This program is a fantastic tool for learning geology, and today, to reinforce the point, I want to show you a couple of examples of Google Earth views replicating almost exactly figures from Chapter 14 of Geology Illustrated: The works of streams and rivers.

The first view is a replica of Figure 130 in the book, showing a fantastic example of a stream (the Colorado River) deepening its valley at the Marble Canyon.

The second view is a replica of Figure 135, showing many excellent examples of stream capture by headward erosion. Notice that in the 60s, when the photo was taken by Shelton, the highway (US Highway 101 north of San Juan Capistrano, California) was the only visible evidence of human activity.

The last view is a replica of Figure 137 in the book, showing the meander belt of the Animas River a few miles from Durango, Colorado. Looking at this was by far my favourite as it gave me the opportunity to create my own time lapse: a repeat snapshots of the same landscape nearly 50 years apart. Tis is priceless: 50 years are nothing in geological time scale, and yet there are already some significant differences in the two images. For example, it looks like the meander cutoff  in the lower left portion of the image had ‘just’ happened in the 60s, whereas at the time the imagery used by Google Earth was acquired (I imagine in the last few years), the remnant oxbow lake is more clearly defined. Another oxbow lake in the center has nearly disappeared.

I found that this process of looking for and replicating the photos in the book, zooming in and out, then in again changing view was a fantastic way to see the geological features as part of the larger geological context, visualize them, see the interconnection with other elements of the landscape, observe how erosion and deposition, and human processes have modeled the landscape in just a few decades (as in the second and third examples).  As a geophysicist, sitting in the office away from the outcrops, this is  invaluable, and a great aid in finding analogs in support of seismic interpretations. And really you don’t need a book in your lap to start the process.

In a future post I will show my results at creating similar views using HD lidar data, which can be downloaded from the National Center for Airborne Laser Mapping, as done in this blog post on Quest.


John Shelton’s obituary, August 2008

Geomorphology from space