Tag Archives: image processing

sketch2model – linking edges with mathematical morphology

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Introduction

As written by Elwyn in the first post of this series, sketch2model was conceived at the 2015 Calgary Geoscience Hackathon as a web and mobile app that would turn an image of geological sketch into a geological model, and then use Agile Geoscience’s modelr.io to create a synthetic seismic model.

original project promo image

The skech2model concept: modelling at the speed of imagination. Take a sketch (a), turn it into an earth model (b), create a forward seismic model (c). Our hack takes you from a to b.

One of the main tasks in sketch2model is to identify each and every geological body in a sketch  as a closed polygon. As Elwyn wrote, “if the sketch were reproduced exactly as imagined, a segmentation function would do a good job. The trouble is that the sketch captured is rarely the same as the one intended – an artist may accidentally leave small gaps between sketch lines, or the sketch medium can cause unintentional effects (for example, whiteboard markers can erase a little when sketch lines cross, see example below). We applied some morphological filtering to compensate for the sketch imperfections.

Morphological filtering can compensate for imperfections in a sketch, as demonstrated in this example. The original sketch (left) was done with a marker on white board. Notice how the vertical stroke erased a small part of the horizontal one. The binarized version of the sketch (middle) shows an unintentional gap between the strokes, but morphological filtering successfully closes the small gap (right).

The cartoon below shows what would be the final output of sketch2model in the two cases in the example above (non closed and closed gap).

My objective with this post is to explain visually how we correct for some of these imperfections within sketch2model. I will focus on the use of morphological closing,  which consist in applying in sequence a dilation and an erosion, the two fundamental morphological operations.

Quick mathematical morphology review

All morphological operations result from the interaction of an image with a structuring element (a kernel) smaller than the image and typically in the shape of a square, disk, or diamond. In most cases the image is binary, that is pixels take either value of 1, for the foreground objects, or 0 for the background. The structuring element operates on the foreground objects.

Morphological erosion is used to remove pixels on the foreground objects’ boundaries. How ‘deeply’ the boundaries are eroded depends on the size of the structuring element (and shape, but in this discussion I will ignore the effect of changing the shape). This operation is in my mind analogous to peeling off a layer from an onion; the thickness of the layer is related to the structuring element size.

Twan Maintz in his book Digital and medical image processing describes the interaction of image and structuring element during erosion this way: place the structuring element anywhere in the image: if it is fully contained in the foreground object (or in one of the objects) then the origin (central) pixel of the structuring element (and only that one) is part of the eroded output. The book has a great example on page 129.

Dilation does the opposite of erosion: it expands the object boundaries (adding pixels) by an amount that is again related to the size of the structuring element. This is analogous to me to adding back a layer to the onion.

Again, thanks to Maintz the interaction of image and structuring element in dilation can be intuitively described: place the structuring element anywhere in the image: does it touch any of the foreground objects? If yes then the origin of the structuring element is part of the dilated result. Great example on pages 127-128.

Closing is then for me akin to adding a layer to an onion (dilation) and then peeling it back off (erosion) but with the major caveat that some of the changes produced by the dilation are irreversible: background holes smaller than the structuring element that are filled by the dilation are not restored by the erosion. Similarly, lines in the input image separated by an amount of pixels smaller than the size of the structuring element are linked by the dilation and not disconnected by the erosion, which is exactly what we wanted for sketch2model.

Closing demo

If you still need further explanation on these morphological operations, I’d recommend reading further on the ImageMagik user guide the sections on erosion, dilation, and closing, and the examples  on the Scikit-image website.

As discussed in the previous section, when applying closing to a binary image, the external points in any object in the input image will be left unchanged in the output, but holes will be filled, partially or completely, and disconnected objects like edges (or lines in sketches) can become connected.

We will now demonstrate it below with Python-made graphics but without code; however,  you can grab the Jupyter notebook with complete Python code on GitHub.

I will use this model binary image containing two 1-pixel wide lines. Think of them as lines in a sketch that should have been connected, but are not.

We will attempt to connect these lines using morphological closing with a disk-shaped structuring element of size 2. The result is plotted in the binary image below, showing that closing was successful.

But what would have happened with a smaller structuring element, or with a larger one? In the case of a disk of size 1, the closing magic did not happen:

Observing this result, one would increase the size of the structuring element. However, as Elwyn will show in the next post, also too big a structuring element would have detrimental effects, causing subsequent operations to introduce significant artifacts in the final results. This has broader implications for our sketch2model app: how do we select automatically (i.e. without hard coding it into the program) the appropriate structuring element size? Again, Elwyn will answer that question; in the last section I want to concentrate on explaining how the closing machinery works in this case.

In the next figure I have broken down the closing operation into its component dilation and erosion, and plotted them step by step to show what happens:

So we see that the edges do get linked by the dilation, but by only one pixel, which the following erosion then removes.

And now let’s break down the closing with disk of size two into its component. This is equivalent to applying two consecutive passes of dilation with disk of size 1, and then two consecutive passes of erosion with disk of size 1, as in the demonstration in the next figure below (by the way, if we observed carefully the second panel above we could predict that the dilation with a disk of size two would result in a link 3-pixel wide instead of 1-pixel wide, which the subsequent erosion will not disconnect).

Below is a GIF animated version of this demo, cycling to the above steps; you can also run it yourself by downloading and running the Jupyter notebook on GitHub.

Additional resources

Closing Jupyter notebook with complete Python code on GitHub

sketch2model Jupyter notebook with complete Python code on GitHub 

More reading on Closing, with examples

Related Posts

sketch2model (2015 Geoscience Hackathon, Calgary)

sketch2model – sketch image enhancements

Mapping and validating geophysical lineaments with Python

sketch2model – sketch image enhancements

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This is the second post of in a series of collaborative articles about sketch2model, a project from the 2015 Calgary Geoscience Hackathon organized by Agile Geoscience.

The first post was written by Elwyn Galloway and published on both his Scibbatical blog and here on MyCarta. In that article Elwyn mentioned the need for an adaptive image conditioning workflow for binarization of photos with geological sketches in images. Binarization is the process of converting a natural image to a binary image (check this simple but awesome interactive demonstration of binarization), which in our case is necessary to separate the sketch from the background.

The following is a demonstration of the preliminary image processing operations applied to the input photo when sketch2model is run. The full code listing of this demonstration is available as a Jupyter notebook on GitHub. Also in GitHub you can find a Jupyter Notebook with the fully documented version of sketch2model.

First we import one of the photos with sketches and convert it to a grayscale image.

im = io.imread('paper_breaks.png')
im = color.rgb2gray(im[0:-1:2,0:-1:2])

Next we enhance the grayscale image with a couple of cascaded processes. But before we do that, let’s graph the intensity values across the image to understand the degree of contrast between sketch edges and background, which ultimately will determine our success in separating them from it. We show this in the figure below, on the left, for one column of pixels (y direction). The black line across the input image on the right shows the location of the column selected. It is fairly obvious from the plot on the left that the intensity of the background is not uniform, due to variable light conditions when the photo was taken, and towards the right (e.g. bottom of the photo) it gets closer to that of the edges. In some images it might even become less than the intensity of the edge. This highlights the need for (preemptively) applying the enhancements illustrated in the remainder of the post.

The first enhancement is called compressor, or limiter. I read many years ago that it is used in electronics to find hard edges in data: the idea is to square each element in the data (image, or other type of data), smooth the result (enough to remove high frequency variations but not so much as to eliminate variability), take the square root, and finally divide each element in the input by the square root result.

I experimented with this method (at the time using Matlab and its Image Processing Toolbox) using the same gravity dataset from my 2015 geophysical tutorial on The Leading Edge (see the post Mapping and validating geophysical lineaments with Python). An example of one such experiments is shown in the figure below where: the top left map is the Bouguer data; the centre top map is the squared data; the top right is the result of a Gaussian blur; the bottom left the result of square root, and centre right is the final output, where the hardest edges in the original data have been enhanced.

The most important parameter in this process is the choice of the smoothing or blur; using a Gaussian kernel of different size more subtle edges are enhanced, as seen in the bottom right map (these are perhaps acquisition-related gridding artifacts).

In our sketch2model implementation the size of the Gaussian kernel is hardcoded; it was chosen following trial and error on multiple photos of sketches and yielded optimal results in the greatest majority of them. We were planning to have the kernel size depend on the size of the input image, but left the implementation to our ‘future work’ list.’

Here’s the compressor code from sketch2model:

# compressor or limiter (electronics): find hard edges in data with long 
# wavelength variations in amplitude
# step 1: square each element in the image to obtain the power function
sqr = im**2
# step 2: gaussian of squared image
flt2 = sp.ndimage.filters.gaussian_filter(sqr,21)
# step 3: divide the intensity of each original pixel by the square root 
# of the smoothed square
cmprs= im/(np.sqrt(flt2))

and a plot of the result (same column of pixels as in the previous one):

From the plot above we see that now the background intensity is uniform and the contrast has been improved. We can maximize it with contrast stretching, as below:

# contrast stretching
p2, p98 = np.percentile(cmprs, (2, 98))
rescale = exposure.rescale_intensity(cmprs, in_range=(p2, p98))

We now have ideal contrast between edges and background, and can get a binary image with the desired sketch edges using a scalar threshold:

# binarize image with scalar threshold
binary = ~(color.rgb2gray(rescale) > 0.5)

Bingo!

sketch2model

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This guest post (first published here) is by Elwyn Galloway, author of Scibbatical on WordPress. It is the first in our series of collaborative articles about sketch2model, a project from the 2015 Calgary Geoscience Hackathon organized by Agile Geoscience. Happy reading.

Collaboration in action. Evan, Matteo, and Elwyn (foreground, L to R) work on sketch2model at the 2015 Calgary Geoscience Hackathon. Photo courtesy of Penny Colton.

Welcome to an epic blog crossover event. Two authors collaborating to tell a single story over the course of several articles.

We’ve each mentioned the sketch2model project on our respective blogs, MyCarta and scibbatical, without giving much detail about it. Apologies if you’ve been waiting anxiously for more. Through the next while, you’ll get to know sketch2model as well as we do.

The sketch2model team came together at the 2015 Geoscience Hackathon (Calgary), hosted by Agile Geoscience. Elwyn and Evan Saltman (epsalt on twitter and GitHub) knew each other from a previous employer, but neither had met Matteo before. All were intrigued by the project idea, and the individual skill sets were diverse enough to combine into a well-rounded group. Ben Bougher, part of the Agile Geoscience team, assisted with the original web interface at the hackathon. Agile’s take on this hackathon can be found on their blog.

Conception

The idea behind sketch2model is that a user should be able to easily create forward seismic models. Modelling at the speed of imagination, allowing seamless transition from idea to synthetic seismic section. It should happen quickly enough to be incorporated into a conversation. It should happen where collaboration happens.

The skech2model concept: modelling at the speed of imagination. Take a sketch (a), turn it into an earth model (b), create a forward seismic model (c). Our hack takes you from a to b.

Geophysicists like to model wedges, and for good reasons. However, wedge logic can get lost on colleagues. It may not effectively demonstrate the capability of seismic data in a given situation. The idea is not to supplant that kind of modeling, but to enable a new, lighter kind of modeling. Modeling that can easily produce results for twelve different depositional scenarios as quickly as they can be sketched on a whiteboard.

The Hack

Building something mobile to turn a sketch into a synthetic seismic section is a pretty tall order for a weekend. We decided to take a shortcut by leveraging an existing project: Agile’s online seismic modelling package, modelr. The fact that modelr works through any web browser (including a smartphone) kept things mobile. In addition, modelr’s existing functionality allows a user to upload a png image and use it as a rock property model. We chose to use a web API to interface our code with the web application (as a bonus, our approach conveniently fit with the hackathon’s theme of Web). Using modelr’s capabilities, our hack was left with the task of turning a photo of a sketched geologic section into a png image where each geologic body is identified as a different color. An image processing project!

Agile is a strong proponent for Python in geophysics (for reasons nicely articulated in their blog post), and the team was familiar with the language to one extent or another. There was no question that it was the language of choice for this project. And no regrets!

We aimed to create an algorithm robust enough to handle any image of anything a user might sketch while accurately reproducing their intent. Marker on whiteboard presents different challenges than pencil on paper. Light conditions can be highly variable. Sketches can be simple or complex, tidy or messy. When a user leaves a small gap between two lines of the sketch, should the algorithm take the sketch as-is and interpret a single body? Or fill the small gap and interpret two separate bodies?

Our algorithm needs to be robust enough to handle a variety of source images: simple, complex, pencil, marker, paper, white board (check out the glare on the bottom left image). These are some of the test images we used.

Matteo has used image processing for geoscience before, so he landed on an approach for our hack almost instantly: binarize the image to distinguish sketch from background (turn color image into a binary image via thresholding); identify and segregate geobodies; create output image with each body colored uniquely.

Taking the image of the original sketch (left) and creating a binary image (right) is an integral part of the sketch2model process.

Python has functions to binarize a color image, but for our applications, the results were very inconsistent. We needed a tool that would work for a variety of media in various lighting conditions. Fortunately, Matteo had some tricks up his sleeve to precondition the images before binarization. We landed on a robust flow that can binarize whatever we throw at it. Matteo will be crafting a blog post on this topic to explain what we’ve implemented.

Once the image is binarized, each geological body must be automatically identified as a closed polygon. If the sketch were reproduced exactly as imagined, a segmentation function would do a good job. The trouble is that the sketch captured is rarely the same as the one intended — an artist may accidentally leave small gaps between sketch lines, or the sketch medium can cause unintentional effects (for example, whiteboard markers can erase a little when sketch lines cross, see example below). We applied some morphological filtering to compensate for the sketch imperfections. If applied too liberally, this type of filtering causes unwanted side effects. Elwyn will explore how we struck a balance between filling unintentional gaps and accurate sketch reproduction in an upcoming blog post.

Morphological filtering can compensate for imperfections in a sketch, as demonstrated in this example. The original sketch (left) was done with a marker on white board. Notice how the vertical stroke erased a small part of the horizontal one. The binarized version of the sketch (middle) shows an unintentional gap between the strokes, but morphological filtering successfully closes the small gap (right).

Compared to the binarization and segmentation, generating the output is a snap. With this final step, we’ve transformed a sketch into a png image where each geologic body is a different color. It’s ready to become a synthetic seismic section in modelr.

Into the Wild

“This is so cool. Draw something on a whiteboard and have a synthetic seismogram right on your iPad five seconds later. I mean, that’s magical.”

Sketch2model was a working prototype by the end of the hackathon. It wasn’t the most robust algorithm, but it worked on a good proportion of our test images. The results were promising enough to continue development after the hackathon. Evidently, we weren’t the only ones interested in further development because sketch2model came up on the February 17th episode of Undersampled Radio. Host Matt Hall: “This is so cool. Draw something on a whiteboard and have a synthetic seismogram right on your iPad five seconds later. I mean, that’s magical.”

Since the hackathon, the algorithm and web interface have progressed to the point that you can use it on your own images at sketch2model.com. To integrate this functionality directly into the forward modelling process, sketch2model will become an option in modelr. The team has made this an open-source project, so you’ll also find it on GitHub. Check out the sketch2model repository if you’re interested in the nuts and bolts of the algorithm. Information posted on these sites is scant right now, but we are working to add more information and documentation.

Sketch2model is designed to enable a new kind of collaboration and creativity in subsurface modelling. By applying image processing techniques, our team built a path to an unconventional kind of forward seismic modelling. Development has progressed to the point that we’ve released it into the wild to see how you’ll use it.

Moiré Patterns

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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.

 

 

Do you know any cool apps?

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I’d like to pick up my Apps page, which I sort of abandoned a while back.

If you have any great app to recommend, I’d love to hear about it so please add them in the comment section to this post. I am looking for Apps for Android and iPhone/iPad in the following categories – ideally free or very low-cost, possibly open-source:

Geology

Geophysics

Cartography and mapping

Planetary Science

Image Processing

Visualization

Edge detection as image fidelity test

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This post is a quick follow-up to Dithering, a very interesting post by Cris Luengo, developer of DIPimage, a free Matlab image analysis toolbox.

Dithering is a graphic method that arranges black and white pixels in an image with certain patterns, to make it appear as though there are many intermediate gray levels. It is used when working with limited palettes. In his post Cris compares several algorithms that perform dithering.

As I commented in the post, after reading it I thought of a way to quantify the effectiveness of the various methods in replicating the original image: we can use Canny and Sobel filters to detect edges on the dithered results, and on the original. I show some of these in the image matrix below:

Looking at these results I argued that the structure-aware dithering did a much better job at preserving the edges in the original and the Canny and Sobel picked up on this (as do our eyes when we look at the results in the top row).

An example of Forensic Image Processing in ImageJ

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In a previous post I introduced ImageJ, a very powerful open source  image processing software. ImageJ allows users to display, edit, analyze, process, and filter images, and its capabilities are greatly increased by hundreds of plugins.

In a future post I will be showing how to use the watershed transform in ImageJ for medical image analysis and advanced geoscience map interpretation and terrain analysis.

Today I am posting a submission entry by guest Ron DeSpain, an image and signal analysis software developer. Ron’s note is about Feature Detection for Fingerprint Matching in ImageJ. I was thrilled to receive this submission as I really have a soft spot for Forensic science. Additionally, it is a nice way to introduce skeletonization, which I will be using in a future series on automatic detection of lineaments in geophysical maps. So, thanks Ron!

Please check this page for reference on fingerprint terminology. And if you are interested in the topic and would like to start a discussion, or make a suggestion,  please use the comment section below. You can also contact Ron directly at ron_despain@hotmail.com if you want to enquire about the code.

==========================================================================================

Initial Feature Detection Steps for Fingerprint Matching – by Ron DeSpain

A common fingerprint pre-processing method called the crossings algorithm is used to extract from a fingerprint features called minutiae.  Minutiae are located at the end of fingerprint ridges and where the ridges split (bifurcations) as shown in Figure 1.  Once detected, minutiae are correlated with a database of known fingerprint minutiae sets.  This article discusses the very first step in detecting these minutiae in a fingerprint.

Figure 1  Types of Fingerprint Minutiae

This fingerprint is available in a free database of fingerprint images at http://bias.csr.unibo.it/fvc2000/download.asp

I got the idea for this convolution based minutiae extractor from a paper similar to Afsar et al. [reference] where a slightly different counting scheme is used to identify minutiae.

This algorithm depends on the fact that the end and bifurcation patterns have unique numbers of crossings in a 3×3 local region, as depicted in Figure 2.  This means that by simply counting the crossings you could detect the minutiae.

Figure 2 Minutiae Patterns

The pseudocode for this algorithm is as follows:

  1. Convert the image to binary, normalized to 0 to 1 range, floating point data
  2. Skeletonize the image
  3. Convolve the skeleton with the unit 3×3 matrix to count the crossings
  4. Multiply the skeletonized image by the convolved image = Features Image
  5. Threshold the Features  image at 2 for ridge ends
  6. Threshold  the Features image  at 4 for bifurcations

The following imageJ macro will identify minutiae using this simple pattern recognition technique.  You can download and install ImageJ free from http://imagej.nih.gov/ij/download.html.  Don’t forget to get the user’s manual and macro coding guide from this site if you want to modify my macro.

//Minutiae Detection Macro
open();
run("Duplicate...", "title=Skeleton");
starttime = getTime();
run("Make Binary");
run("Skeletonize");
run("32-bit");
run("Divide...", "value=255.000");
run("Enhance Contrast", "saturated=0 normalize");
run("Duplicate...", "title=Convolution");
run("Convolve...", "text1=[1 1 1\n1 1 1\n1 1 1\n] stack");
imageCalculator("Multiply create 32-bit", "Skeleton","Convolution");
endtime = getTime();
selectWindow("Result of Skeleton");
rename("Features");
run("Tile");
run("Threshold...");
print("Processing Time (ms) = "+(endtime - starttime));
setTool(11);
selectWindow("Features");
run("Sync Windows");

Copy this code to a text file (.txt), drop it into the ImageJ macros folder, install and run it in ImageJ using the image at the end of this article.

The output of the above macro is shown in Figure 3 below:

Figure 3 ImageJ Macro Output

Setting the threshold control to show pixels with a value of 2 in red highlights will show the ridge end detections as shown in Figure 4.   Note that the noise in the image produces false detections, which have to be identified with further processing not addressed here.

Figure 4 Ridge End Detections

Bifurcations are similarly found by setting the threshold to 4 as shown in Figure 5:

Figure 5 Bifurcations Detected

There are two fingerprint processing macros on the Mathworks user community file exchange for Matlab users and free fingerprint verification SDK at http://www.neurotechnology.com/free-fingerprint-verification-sdk.html  for those of you who would like to dig deeper into this subject.

You can copy and save the fingerprint image I used in this article directly from this document’s Figure 6 to get you started either via screen capture, or right-click the image download.

Figure 6  Original Image

Reference

Afsar, F. A., M. Arif, and M. Hussain. “Fingerprint identification and verification system using minutiae matching.” National Conference on Emerging Technologies. 2004.

Lending you a hand with impage processing – introduction to ImageJ

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In a previous post I used an x-ray of my left hand to showcase some basic image visualization techniques in Matlab.

If you are interested in learning image processing and analysis on your own (just like I did) but are not too interested in the programming side of things or would rather find a noncommercial alternative I’d recommend ImageJ. I just stumbled into it a few weeks ago and was immediately drawn to it.

ImageJ is a completely free, open source, Java-based image processing environment. It allows users to display, edit, analyze, process, and filter images, and its capabilities are greatly increased by hundreds of plugins on the official webpage and elsewhere.

It is used extensively by biomedical and medical image processing professionals (check this fantastic tutorial by the Montpellier RIO imaging lab), but is popular in many fields, from A-stronomy (you can read a brief review in here) to Z-oology (check this site).

I decided to give it a try right away. Within an hour of installing it on my iMac I had added the Interactive 3D SurfacePlot plugin, loaded the hand x-ray image, displayed it and adjusted the z scale, smoothing, lighting, and intensity thresholds to what (preliminarily) seemed optimal.

For each discrete adjustment I saved a screen capture, then I reimported as an image sequence in ImageJ and easily saved the sequence as an AVI movie, which is here below. I’m hoping this will give you a sense of how I iteratively converged to a good result.

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