Algorithm for scaling irregular polygons - python

A syntax called 'gcode' is used to tell CNC engraving machines how to move.
An example of gcode is as follows :
G00 Z1 F800 (lift z axis by 1mm)
G00 X49.546785 Y-11.48703 F800 (Go to these coordinates at 800mm/m)
G01 Z-0.35 F100 (Penetrate. Lower the tool into the work by 0.35mm)
G03 X49.126859 Y-11.464812 I-0.385599 J-3.308393 F80 (cut an anticlockwise arc at 80mm/m)
(arc ends at X,Y, arc centre is x+i, y+j)
etc.
As you can see we can describe the movement of the tool in stright lines (G0,G1) and in arcs (G2,G3) from coordinates in the x,y and z planes.
Using this mechanism we can draw (engrave) paths, often they are closed paths as below:
In this image we see a closed path (letter a) in black. The green outline is the same path but 'scaled upwards' and the red path is the same path but scaled downwards.
In Inkscape we can do this using the 'dynamic offset' tool.
I am looking for an algorithm I can apply to gcode (as described above) to scale paths as described.
My first thought is literally to just scale every single line and arc :
Say we are scaling by 'n'%
Essentially we would make every line n% longer, and every arc n% bigger.
But what would the resulting path centre on?
Does anyone know the name of this algorithm, or have any links or examples of how to achieve this in say, SVG or any other coordinate based system (preferably in python if possible).
Addendum :
The process of scaling polygons inwards and outwards largely has two distinct names: 'Dilation' and 'offsetting'.
See here for a near answer to this question

As given in the comments, Dilation, Erosion, Opening and Closing are standard morphology operations. In fact, the graphic at Wikipedia gives details that are quite similar to what you have.
The difference is that the inside of the object is included in the dilation and erosion. Just alter the structuring element size and you can subtract the images to get the traces that you want.
The erosion and dilation are simpler forms of morphology, so look at those first to understand the algorithms. They are implemented in OpenCV which has Python bindings; however, they are fairly simple to code.
It maybe possible to use XOR to get the outline without image subtraction. But simply the perimeter of the opening and closing is the outline that I think you are looking for. Dilation and erosion will give slightly different paths. You could also use Voronoi partitioning, as a crudest form. The main difference is how corners and other junctions are handled.

Related

Skewing text - How to take advantage of existing edges

I have the following JPG image. If I want to find the edges where the white page meets the black background. So I can rotate the contents a few degrees clockwise. My aim is to straighten the text for using with Tesseract OCR conversion. I don't see the need to rotate the text blocks as I have seen in similar examples.
In the docs Canny Edge Detection the third arg 200 eg edges = cv.Canny(img,100,200) is maxVal and said to be 'sure to be edges'. Is there anyway to determine these (max/min) values ahead of any trial & error approach?
I have used code examples which utilize the Python cv2 module. But the edge detection is set up for simpler applications.
Is there any approach I can use to take the text out of the equation. For example: only detecting edge lines greater than a specified length?
Any suggestions would be appreciated.
Below is an example of edge detection (above image same min/max values) The outer edge of the page is clearly defined. The image is high contrast b/w. It has even lighting. I can't see a need for the use of an adaptive threshold. Simple global is working. Its just at what ratio to use it.
I don't have the answer to this yet. But to add. I now have the contours of the above doc.
I used find contours tutorial with some customization of the file loading. Note: removing words gives a thinner/cleaner outline.
Consider Otsu.
Its chief virtue is that it is adaptive to local
illumination within the image.
In your case, blank margins might be the saving grace.
Consider working on a series of 2x reduced resolution images,
where new pixel is min() (or even max()!) of original four pixels.
These reduced images might help you to focus on the features
that matter for your use case.
The usual way to deskew scanned text is to binarize and
then keep changing theta until "sum of pixels across raster"
is zero, or small. In particular, with few descenders
and decent inter-line spacing, we will see "lots" of pixels
on each line of text and "near zero" between text lines,
when theta matches the original printing orientation.
Which lets us recover (1.) pixels per line, and (2.) inter-line spacing, assuming we've found a near-optimal theta.
In your particular case, focusing on the ... leader dots
seems a promising approach to finding the globally optimal
deskew correction angle. Discarding large rectangles of
pixels in the left and right regions of the image could
actually reduce noise and enhance the accuracy of
such an approach.

Find pixel coordinates of grid intersection points

I am trying to find a repeatable process to find the coordinates of grid intersection points from an image. The image is a montage of many smaller images. Each 'tile' of the montage has inconsistent contrast, so my naive methods are failing (the tile boundary is being selected) . A small example:
I have had minor advances from the ideas explained in How to remove convexity defects in a Sudoku square? and Grid detection in matlab
However, the grid lines are NOT necessarily straight over the entire image, so cannot approximate as a grid of straight lines. I am familiar with imageJ or Gatan digitalMicrograph software, if anyone knows of a simple solution. Otherwise matlab/python Opencv would be useful
My first idea: write a script to chop your image into tiles, and apply some contrast normalization such as CLAHE to each one. Then reassemble the tiles using the Stitching plugin with the Linear Blending option on, to avoid the sharp tile lines. After that, segmenting the grid will become much easier; see ImageJ's Segmentation page for an introduction.
This is the kind of image analysis problem that is better discussed on the ImageJ Forum where people can throw ideas and script snippets back and forth, to converge on a solution.

Detect grid nodes using OpenCV (or using something else)

I have a grid on pictures (they are from camera). After binarization they look like this (red is 255, blue is 0):
What is the best way to detect grid nodes (crosses) on these pictures?
Note: grid is distorted from cell to cell non-uniformly.
Update:
Some examples of different grids and thier distortions before binarization:
In cases like this I first try to find the best starting point.
So, first I thresholded your image (however I could also skeletonize it and just then threshold. But this way some data is lost irrecoverably):
Then, I tried loads of tools to get the most prominent features emphasized in bulk. Finally, playing with Gimp's G'MIC plugin I found this:
Based on the above I prepared a universal pattern that looks like this:
Then I just got a part of this image:
To help determine angle I made local Fourier freq graph - this way you can obtain your pattern local angle:
Then you can make a simple thick that works fast on modern GPUs - get difference like this (missed case):
When there is hit the difference is minimal; what I had in mind talking about local maximums refers more or less to how the resulting difference should be treated. It wouldn't be wise to weight outside of the pattern circle difference the same as inside due to scale factor sensitivity. Thus, inside with cross should be weighted more in used algorithm. Nevertheless differenced pattern with image looks like this:
As you can see it's possible to differentiate between hit and miss. What is crucial is to set proper tolerance and use Fourier frequencies to obtain angle (with thresholded images Fourier usually follows overall orientation of image analyzed).
The above way can be later complemented by Harris detection, or Harris detection can be modified using above patterns to distinguish two to four closely placed corners.
Unfortunately, all techniques are scale dependent in such case and should be adjusted to it properly.
There are also other approaches to your problem, for instance by watershedding it first, then getting regions, then disregarding foreground, then simplifying curves, then checking if their corners form a consecutive equidistant pattern. But to my nose it would not produce correct results.
One more thing - libgmic is G'MIC library from where you can directly or through bindings use transformations shown above. Or get algorithms and rewrite them in your app.
I suppose that this can be a potential answer (actually mentioned in comments): http://opencv.itseez.com/2.4/modules/imgproc/doc/feature_detection.html?highlight=hough#houghlinesp
There can also be other ways using skimage tools for feature detection.
But actually I think that instead of Hough transformation that could contribute to huge bloat and and lack of precision (straight lines), I would suggest trying Harris corner detection - http://docs.opencv.org/2.4/doc/tutorials/features2d/trackingmotion/harris_detector/harris_detector.html .
This can be further adjusted (cross corners, so local maximum should depend on crossy' distribution) to your specific issue. Then some curves approximation can be done based on points got.
Maybe you cloud calculate Hough Lines and determine the intersections. An OpenCV documentation can be found here

Pipeline to create Voronoi Meshes

I would like to implement a Maya plugin (this question is independent from Maya) to create 3D Voronoi patterns, Something like
I just know that I have to start from point sampling (I implemented the adaptive poisson sampling algorithm described in this paper).
I thought that, from those points, I should create the 3D wire of the mesh applying Voronoi but the result was something different from what I expected.
Here are a few example of what I get handling the result i get from scipy.spatial.Voronoi like this (as suggested here):
vor = Voronoi(points)
for vpair in vor.ridge_vertices:
for i in range(len(vpair) - 1):
if all(x >= 0 for x in vpair):
v0 = vor.vertices[vpair[i]]
v1 = vor.vertices[vpair[i+1]]
create_line(v0.tolist(), v1.tolist())
The grey vertices are the sampled points (the original shape was a simple sphere):
Here is a more complex shape (an arm)
I am missing something? Can anyone suggest the proper pipeline and algorithms I have to implement to create such patterns?
I saw your question since you posted it but didn’t have a real answer for you, however as I see you still didn’t get any response I’ll at least write down some ideas from me. Unfortunately it’s still not a full solution for your problem.
For me it seems you’re mixing few separate problems in this question so it would help to break it down to few pieces:
Voronoi diagram:
The diagram is by definition infinite, so when you draw it directly you should expect a similar mess you’ve got on your second image, so this seems fine. I don’t know how the SciPy does that, but the implementation I’ve used flagged some edge ends as ‘infinite’ and provided me the edges direction, so I could clip it at some distance by myself. You’ll need to check the exact data you get from SciPy.
In the 3D world you’ll almost always want to remove such infinite areas to get any meaningful rendering, or at least remove the area that contains your camera.
Points generation:
The Poisson disc is fine as some sample data or for early R&D but it’s also the most boring one :). You’ll need more ways to generate input points.
I tried to imagine the input needed for your ball-like example and I came up with something like this:
Create two spheres of points, with the same center but different radius.
When you create a Voronoi diagram out of it and remove infinite areas you should end up with something like a football ball.
If you created both spheres randomly you’ll get very irregular boundaries of the ‘ball’, but if you scale the points of one sphere, to use for the 2nd one you should get a regular mesh, similar to ball. You can also use similar points, but add some random offset to control the level of surface irregularity.
Get your computed diagram and for each edge create few points along this edge - this will give you small areas building up the edges of bigger areas. Play with random offsets again. Try to ignore edges, that doesn't touch any infinite region to get result similar to your image.
Get the points from both stages and compute the diagram once more.
Mesh generation:
Up to now it didn’t look like your target images. In fact it may be really hard to do it with production quality (for a Maya plugin) but I see some tricks that may help.
What I would try first would be to get all my edges and extrude some circle along them. You may modulate circle size to make it slightly bigger at the ends. Then do Boolean ‘OR’ between all those meshes and some Mesh Smooth at the end.
This way may give you similar results but you’ll need to be careful at mesh intersections, they can get ugly and need some special treatment.

Image Segmentation based on Pixel Density

I need some help developing some code that segments a binary image into components of a certain pixel density. I've been doing some research in OpenCV algorithms, but before developing my own algorithm to do this, I wanted to ask around to make sure it hasn't been made already.
For instance, in this picture, I have code that imports it as a binary image. However, is there a way to segment objects in the objects from the lines? I would need to segment nodes (corners) and objects (the circle in this case). However, the object does not necessarily have to be a shape.
The solution I thought was to use pixel density. Most of the picture will made up of lines, and the objects have a greater pixel density than that of the line. Is there a way to segment it out?
Below is a working example of the task.
Original Picture:
Resulting Images after Segmentation of Nodes (intersection of multiple lines) and Components (Electronic components like the Resistor or the Voltage Source in the picture)
You can use an integral image to quickly compute the density of black pixels in a rectangular region. Detection of regions with high density can then be performed with a moving window in varying scales. This would be very similar to how face detection works but using only one super-simple feature.
It might be beneficial to make all edges narrow with something like skeletonizing before computing the integral image to make the result insensitive to wide lines.
OpenCV has some functionality for finding contours that is able to put the contours in a hierarchy. It might be what you are looking for. If not, please add some more information about your expected output!
If I understand correctly, you want to detect the lines and the circle in your image, right?
If it is the case, have a look at the Hough line transform and Hough circle transform.

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