Best-fit hexagonal tilings of irregular areas - image-processing

I'm looking for recommendations for an application or library to calculate good fits of regular hexagonal grids to an irregular area or group of areas.
Minimally, I'd like to be able to supply an image and maximum number of hexagons and retrieve the image that rotates/shifts/scales a hexagonal grid to fill each hexagon with one color with minimal error. An advanced feature might be to perform deformations of the underlying image (within specified limits) to achieve a better fit. I have some ideas of how I'd do this myself, but it seems likely to be a solved problem.
Thanks for any suggestions.
EDIT: The use-case I'm thinking of would be to generate reasonably faithful hex maps of real geography for use in board (or virtual board) games.

My general idea is to do the following:
you should to approximate your irregular Curve shape to a minimal linear segments
then, you may calculate the angle a between each couple of sements 90 < a <180.
There are few methods to approximate curves into lines: explained here

Related

OpenCV compare similar hand drawn images

I am trying to compare two mono-chrome, basic hand drawn images, captured electronically. The scale may be different but the essences of the image is the same. I want to compare one hand drawn image to a save library of images and get a relative score of how similar they are. Think of several basic geometric shapes, lines, and curves that make up a drawing.
I have tried several techniques without much luck. Pixel based comparisons are too exact. I have tried scaling and cropping images and that did not get accurate results.
I have tried OpenCV with C# and have had a little success. I have experimented with SURF and it works for a few images, but not others that the eye can tell are very similar.
So now my question: Are there any examples of using openCV or commercial software that can support comparing drawings that are not exact? I prefer C# but I am open to any solutions.
Thanks in advance for any guidance.
(I have been working on this for over a month and have searched the internet and Stack Overflow without success. I of course could have missed something)
You need to extract features from these images and after that using a basic euclidean distance would be enough to calculate similarity. But hand writtend drawn thins are not easy to extract features. For example, companies that work on face recognition generally have much less accuracy on drawn face portraits.
I have a suggestion for you. For a machine learning homework, one of my friends got the signature recognition assingment. I do not fully know how he did it with a high accuracy, but I know feature extraction part. Firtstly he converted it to binary image. And than he calculated the each row's black pixel count. Than he used that features to train a NN or etc.
So you can use this similar approach to extract features. Than use a euclidean distance to calculate similarities.

how to find shapes that are slightly elongated oval / rectangle with curved corners / sometimes sector of a circle?

how to recognise a zebra crossing from top view using opencv?
in my previous question the problem is to find the curved zebra crossing using opencv.
now I thought that the following way would be much easier way to detect it,
(i) canny it
(ii) find the contours in it
(iii) find the black stripes in it, in my case it is slightly oval in shape
now my question is how to find that slightly oval shape??
look here for images of the crossing: www.shaastra.org/2013/media/events/70/Tab/422/Modern_Warfare_ps_v1.pdf
Generally speaking, I believe there are two approaches you can consider.
One approach is the more brute force image analysis approach, as you described. Here you are applying heuristics based on your knowledge of the problem in order to identify the pixels involved in the parts of the path. Note that 'brute force' here is not a bad thing, just an adjective.
An alternative approach is to apply pattern recognition techniques to find the regions of the image which have high probability of being part of the path. Here you would be transforming your image into (hopefully) meaningful features: lines, points, gradient (eg: Histogram of Oriented Gradients (HOG)), relative intensity (eg: Haar-like features) etc. and using machine learning techniques to figure out how these features describe the, say, the road vs the tunnel (in your example).
As you are asking about the former, I'm going to focus on that here. If you'd like to know more about the latter have a look around the Internet, StackOverflow, or post specific questions you have.
So, for the 'brute force image analysis' approach, your first step would probably be to preprocess the image as you need;
Consider color normalization if you are going to analyze color later, this will help make your algorithm robust to lighting differences in your garage vs the event studio. It'll also improve robustness to camera collaboration differences, though the organization hosting the competition provide specs for the camera they will use (don't ignore this bit of info).
Consider blurring the image to reduce noise if you're less interested in pixel by pixel values (eg edges) and more interested in larger structures (eg gradients).
Consider sharpening the image for the opposite reasons of blurring.
Do a bit of research on image preprocessing. It's definitely an explored topic but hardly 'solved' (whatever that would mean). There are lots of things to try at this stage and, of course, crap in => crap out.
After that you'll want to generate some 'features'..
As you mentioned, edges seem like an appropriate feature space for this problem. Don't forget that there are many other great edge detection algorithms out there other than Canny (see Prewitt, Sobel, etc.) After applying the edge detection algorithm, though, you still just have pixel data. To get to features you'll want probably want to extract lines from the edges. This is where the Hough transform space will come in handy.
(Also, as an idea, you can think about colorspace in concert with the edge detectors. By that, I mean, edge detectors usually work in the B&W colorspace, but rather than converting your image to grayscale you could convert it to an appropriate colorspace and just use a single channel. For example, if the game board is red and the lines on the crosswalk are blue, convert the image to HSV and grab the hue channel as input for the edge detector. You'll likely get better contrast between the regions than just grayscale. For bright vs. dull use the value channel, for yellow vs. blue use the Opponent colorspace, etc.)
You can also look at points. Algorithms such as the Harris corner detector or the Laplacian of Gaussian (LOG) will extract 'key points' (with a different definition for each algorithm but generally reproducible).
There are many other feature spaces to explore, don't stop here.
Now, this is where the brute force part comes in..
The first thing that comes to mind is parallel lines. Even in a curve, the edges of the lines are 'roughly' parallel. You could easily develop an algorithm to find the track in your game by finding lines which are each roughly parallel to their neighbors. Note that line detectors like the Hough transform are usually applied such that they find 'peaks', or overrepresented angles in the dataset. Thus, if you generate a Hough transform for the whole image, you'll be hard pressed to find any of the lines you want. Instead, you'll probably want to use a sliding window to examine each area individually.
Specifically speaking to the curved areas, you can use the Hough transform to detect circles and elipses quite easily. You could apply a heuristic like: two concentric semi-circles with a given difference in radius (~250 in your problem) would indicate a road.
If you're using points/corners you can try to come up with an algorithm to connect the corners of one line to the next. You can put a limit on the distance and degree in rotation from one corner to the next that will permit rounded turns but prohibit impossible paths. This could elucidate the edges of the road while being robust to turns.
You can probably start to see now why these hard coded algorithms start off simple but become tedious to tweak and often don't have great results. Furthermore, they tend to rigid and inapplicable to other, even similar, problems.
All that said.. you're talking about solving a problem that doesn't have an out of the box solution. Thinking about the solution is half the fun, and half the challenge. Everything I've described here is basic image analysis, computer vision, and problem solving. Start reading some papers on these topics and the ideas will come quickly. Good luck in the competition.

Algorithm for capturing machine readable zones

What method is suitable to capture (detect) MRZ from a photo of a document? I'm thinking about cascade classifier (e.g. Viola-Jones), but it seems a bit weird to use it for this problem.
If you know that you will look for text in a passport, why not try to find passport model points on it first. Match template of a passport to it by using ASM/AAM (Active shape model, Active Appearance Model) techniques. Once you have passport position information you can cut out the regions that you are interested in. This will take some time to implement though.
Consider this approach as a great starting point:
Black top-hat followed by a horisontal derivative highlights long rows of characters.
Morphological closing operation(s) merge the nearby characters and character rows together into a single large blob.
Optional erosion operation(s) remove the small blobs.
Otsu thresholding followed by contour detection and filtering away the contours which are apparently too small, too round, or located in the wrong place will get you a small number of possible locations for the MRZ
Finally, compute bounding boxes for the locations you found and see whether you can OCR them successfully.
It may not be the most efficient way to solve the problem, but it is surprisingly robust.
A better approach would be the use of projection profile methods. A projection profile method is based on the following idea:
Create an array A with an entry for every row in your b/w input document. Now set A[i] to the number of black pixels in the i-th row of your original image.
(You can also create a vertical projection profile by considering columns in the original image instead of rows.)
Now the array A is the projected row/column histogram of your document and the problem of detecting MRZs can be approached by examining the valleys in the A histogram.
This problem, however, is not completely solved, so there are many variations and improvements. Here's some additional documentation:
Projection profiles in Google Scholar: http://scholar.google.com/scholar?q=projection+profile+method
Tesseract-ocr, a great open source OCR library: https://code.google.com/p/tesseract-ocr/
Viola & Jones' Haar-like features generate many (many (many)) features to try to describe an object and are a bit more robust to scale and the like. Their approach was a unique approach to a difficult problem.
Here, however, you have plenty of constraint on the problem and anything like that seems a bit overkill. Rather than 'optimizing early', I'd say evaluate the standard OCR tools off the shelf and see where they get you. I believe you'll be pleasantly surprised.
PS:
You'll want to preprocess the image to isolate the characters on a white background. This can be done quite easily and will help the OCR algorithms significantly.
You might want to consider using stroke width transform.
You can follow these tips to implement it.

Shape/Pattern Matching Approach in Computer Vision

I am currently facing a, in my opinion, rather common problem which should be quite easy to solve but so far all my approached have failed so I am turning to you for help.
I think the problem is explained best with some illustrations. I have some Patterns like these two:
I also have an Image like (probably better, because the photo this one originated from was quite poorly lit) this:
(Note how the Template was scaled to kinda fit the size of the image)
The ultimate goal is a tool which determines whether the user shows a thumb up/thumbs down gesture and also some angles in between. So I want to match the patterns against the image and see which one resembles the picture the most (or to be more precise, the angle the hand is showing). I know the direction in which the thumb is showing in the pattern, so if i find the pattern which looks identical I also have the angle.
I am working with OpenCV (with Python Bindings) and already tried cvMatchTemplate and MatchShapes but so far its not really working reliably.
I can only guess why MatchTemplate failed but I think that a smaller pattern with a smaller white are fits fully into the white area of a picture thus creating the best matching factor although its obvious that they dont really look the same.
Are there some Methods hidden in OpenCV I havent found yet or is there a known algorithm for those kinds of problem I should reimplement?
Happy New Year.
A few simple techniques could work:
After binarization and segmentation, find Feret's diameter of the blob (a.k.a. the farthest distance between points, or the major axis).
Find the convex hull of the point set, flood fill it, and treat it as a connected region. Subtract the original image with the thumb. The difference will be the area between the thumb and fist, and the position of that area relative to the center of mass should give you an indication of rotation.
Use a watershed algorithm on the distances of each point to the blob edge. This can help identify the connected thin region (the thumb).
Fit the largest circle (or largest inscribed polygon) within the blob. Dilate this circle or polygon until some fraction of its edge overlaps the background. Subtract this dilated figure from the original image; only the thumb will remain.
If the size of the hand is consistent (or relatively consistent), then you could also perform N morphological erode operations until the thumb disappears, then N dilate operations to grow the fist back to its original approximate size. Subtract this fist-only blob from the original blob to get the thumb blob. Then uses the thumb blob direction (Feret's diameter) and/or center of mass relative to the fist blob center of mass to determine direction.
Techniques to find critical points (regions of strong direction change) are trickier. At the simplest, you might also use corner detectors and then check the distance from one corner to another to identify the place when the inner edge of the thumb meets the fist.
For more complex methods, look into papers about shape decomposition by authors such as Kimia, Siddiqi, and Xiaofing Mi.
MatchTemplate seems like a good fit for the problem you describe. In what way is it failing for you? If you are actually masking the thumbs-up/thumbs-down/thumbs-in-between signs as nicely as you show in your sample image then you have already done the most difficult part.
MatchTemplate does not include rotation and scaling in the search space, so you should generate more templates from your reference image at all rotations you'd like to detect, and you should scale your templates to match the general size of the found thumbs up/thumbs down signs.
[edit]
The result array for MatchTemplate contains an integer value that specifies how well the fit of template in image is at that location. If you use CV_TM_SQDIFF then the lowest value in the result array is the location of best fit, if you use CV_TM_CCORR or CV_TM_CCOEFF then it is the highest value. If your scaled and rotated template images all have the same number of white pixels then you can compare the value of best fit you find for all different template images, and the template image that has the best fit overall is the one you want to select.
There are tons of rotation/scaling independent detection functions that could conceivably help you, but normalizing your problem to work with MatchTemplate is by far the easiest.
For the more advanced stuff, check out SIFT, Haar feature based classifiers, or one of the others available in OpenCV
I think you can get excellent results if you just compute the two points that have the furthest shortest path going through white. The direction in which the thumb is pointing is just the direction of the line that joins the two points.
You can do this easily by sampling points on the white area and using Floyd-Warshall.

square detection, image processing

I am looking for an efficient way to detect the small boxes around the numbers (see images)?
I already tried to use hough transformation with no success. Any ideas? I need some hints! I am using opencv...
For inspiration, you can have a look at the
Matlab video sudoku solver demo and explanation
Sudoku Grab, an Iphone App, whose author explains the computer vision part on his blog
Alternatively, if you are always hunting for the same grid you could deploy something like this:
Make a perfect artificial template of the grid and detect or save all coordinates from all corners.
In the target image, do the same thing, for example with Harris points. Be creative, you might also be able to use the distinct triangles that can be found in your images.
Using the coordinates from the template and the found harris points, determine the affine transformation x = Ax' between the template and the target image. That transformation can then be used to map the template grid onto the target image. At the very least this will give you some prior information to help guide further segmentation.
The gist of the idea and examples of the estimation of affine matrix A can be found on the site of Zissermans book Multiple View Geometry in Computer Vision and Peter Kovesi
I'd start by trying to detect the rectangular boundary of the overall sheet, then applying a perspective transform to make it truly rectangular. Crop that portion of the image out. If possible, then try to make the alternating white and grey sub-rectangles have an equal background brightness - maybe try adaptive histogram equalization.
Then the Hough transform might perform better. Alternatively, you could then take an approach that's broadly similar to this demonstration by Robert Bemis on MATLAB Central (it's analysing a DNA microarray image rather than Lotto cards, but it's essentially finding bounding boxes of items arranged in a grid). At a high level, the approach is to calculate the autocorrelation along columns and rows of pixels to detect the periodicity of the items in the grid, and use that to impose a bounding box on each item.
Sorry the above advice is mostly MATLAB-based; I'm afraid I'm not an opencv user, but hopefully it will give you some ideas at least.

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