Our aim, find vanishing point of rectangular shape. I want to apply hough transform this shape with y=mx+c. Than, after hough transform, I have to show two or more vote points on (m,c) axis second shape. I dont know how I apply. please help me.
The idea of Hough transform is that you basically draw all possible lines and then try to figure out which ones are really present in the image.
So, for your images, try to draw all possible horizontal/vertical lines and count the black points under each. Fot example - take horizontal line with y = 0(1,2,3..). Check the color of all points with x=[0...width] and y=0. If all or most of them are black - you have a line. Repeat with y=[1...height].
After you have the coordinates of all lines, you can find the gaps in each line in the same fashion - check all the points that should belong to the line and note the white ones. When you have enough white points in a row - there is a gap.
This method will help detecting few points of a figure on your first picture. Then you just have to connect them together to get your shape.
Related
I have a situation where I have a set of pixels that make up the border of a quadrilateral (very close to square). I'm trying to determine the location of the corners as best as possible and have been struggling for a while now. My first thought was to determine the straight lines of the border and then calculate the corner points, but I don't have access to OpenCV or other image processing libraries, unfortunately.
Below are three cases where the black outline is the image boundary and the red outline is the quadrilateral boundary. I have a list of all of the pixels that make up the red boundary and the red boundary thickness may vary.
My initial thought was that I could just find the pixel that is closest to each of the four image boundaries, however this won't quite work for the first case where the inner quadrilateral isn't tilted.
Any thoughts on how to tackle this problem would be great. I'm coding in dart, but am looking for a psuedocode answer that I can implement myself.
(I have seen this post, which is similar to my problem, but I think there should be a simpler solution for my problem since I have access to all of the boundary points of the quadrilateral)
Having a list of all rectangle boundary pixels, you can use simple methods like this:
Calculate gravity center of rectangle (just sum X- and Y- coordinates of pixels and divide by their number) - it is diagonal intersection.
Find the farthest pixels - they are corners.
In case of bad quality of data set (empty places, excessive pixels) center calculation might be inexact. So you can apply Hough transform to extract sides (as lines) and calculate their intersections.
I have many images like the following (only white and black):
My final problem is to find well matching ellipses. Unfortunately the real used images are not always that nice like this. They could be deformed a bit, which makes ellipse matching probably harder.
My idea is to find "break points". I markes them in the following picture:
Maybe these points could help to make a matching for the ellipses. The end result should be something like this:
Has someone an idea what algorithm may be used to find these break points? Or even better to make good ellipse matching?
Thank you very much
Sample the circumference points
Just scan your image and select All Black pixels with any White neighbor. You can do this by recoloring the remaining black pixels to any unused color (Blue).
After whole image is done you can recolor the inside back from unused color (Blue) to white.
form a list of ordered circumference points per cluster/ellipse
Just scan your image and find first black pixel. Then use A* to order the circumference points and store the path in some array or list pnt[] and handle it as circular array.
Find the "break points"
They can be detect by peak in the angle between neighbors of found points. something like
float a0=atan2(pnt[i].y-pnt[i-1].y,pnt[i].x-pnt[i-1].x);
float a1=atan2(pnt[i+1].y-pnt[i].y,pnt[i+1].x-pnt[i].x);
float da=fabs(a0-a1); if (da>M_PI) da=2.0*M_PI-da;
if (da>treshold) pnt[i] is break point;
or use the fact that on break point the slope angle delta change sign:
float a1=atan2(pnt[i-1].y-pnt[i-2].y,pnt[i-1].x-pnt[i-2].x);
float a1=atan2(pnt[i ].y-pnt[i-1].y,pnt[i ].x-pnt[i-1].x);
float a2=atan2(pnt[i+1].y-pnt[i ].y,pnt[i+1].x-pnt[i ].x);
float da0=a1-a0; if (da0>M_PI) da0=2.0*M_PI-da0; if (da0<-M_PI) da0=2.0*M_PI+da0;
float da1=a2-a1; if (da1>M_PI) da1=2.0*M_PI-da1; if (da1<-M_PI) da1=2.0*M_PI+da1;
if (da0*da1<0.0) pnt[i] is break point;
fit ellipses
so if no break points found you can fit the entire pnt[] as single ellipse. For example Find bounding box. It's center is center of ellipse and its size gives you semi-axises.
If break points found then first find the bounding box of whole pnt[] to obtain limits for semi-axises and center position area search. Then divide the pnt[] to parts between break points. Handle each part as separate part of ellipse and fit.
After all the pnt[] parts are fitted check if some ellipses are not the same for example if they are overlapped by another ellipse the they would be divided... So merge the identical ones (or average to enhance precision). Then recolor all pnt[i] points to white, clear the pnt[] list and loop #2 until no more black pixel is found.
how to fit ellipse from selection of points?
algebraically
use ellipse equation with "evenly" dispersed known points to form system of equations to compute ellipse parameters (x0,y0,rx,ry,angle).
geometrically
for example if you detect slope 0,90,180 or 270 degrees then you are at semi-axis intersection with circumference. So if you got two such points (one for each semi-axis) that is all you need for fitting (if it is axis-aligned ellipse).
for non-axis-aligned ellipses you need to have big enough portion of the circumference available. You can exploit the fact that center of bounding box is also the center of ellipse. So if you got the whole ellipse you know also the center. The semi-axises intersections with circumference can be detected with biggest and smallest tangent change. If you got center and two points its all you need. In case you got only partial center (only x, or y coordinate) you can combine with more axis points (find 3 or 4)... or approximate the missing info.
Also the half H,V lines axis is intersecting ellipse center so it can be used to detect it if not whole ellipse in the pnt[] list.
approximation search
You can loop through "all" possible combination of ellipse parameters within limits found in #4 and select the one that is closest to your points. That would be insanely slow of coarse so use binary search like approach something like mine approx class. Also see
Curve fitting with y points on repeated x positions (Galaxy Spiral arms)
on how it is used for similar fit to yours.
hybrid
You can combine geometrical and approximation approach. First compute what you can by geometrical approach. And then compute the rest with approximation search. you can also increase precision of the found values.
In rare case when two ellipses are merged without break point the fitted ellipse will not match your points. So if such case detected you have to subdivide the used points into groups until their fits matches ...
This is what I have in mind with this:
You probably need something like this:
https://en.wikipedia.org/wiki/Circle_Hough_Transform
Your edge points are simply black pixels with at least one white 4-neighbor.
Unfortunately, though, you say that your ellipses may be “tilted”. Generic ellipses are described by quadratic equations like
x² + Ay² + Bxy + Cx + Dy + E = 0
with B² < 4A (⇒ A > 0). This means that, compared to the circle problem, you don't have 3 dimensions but 5. This causes the Hough transform to be considerably harder. Luckily, your example suggests that you don't need a high resolution.
See also: algorithm for detecting a circle in an image
EDIT
The above idea for an algorithm was too optimistic, at least if applied in a straightforward way. The good news is that it seems that two smart guys (Yonghong Xie and Qiang Ji) have already done the homework for us:
https://www.ecse.rpi.edu/~cvrl/Publication/pdf/Xie2002.pdf
I'm not sure I would create my own algorithm. Why not leverage the work other teams have done to figure out all that curve fitting of bitmaps?
INKSCAPE (App Link)
Inkscape is an open source tool which specializes in vector graphics editing with some ability to work with raster (bitmap) parts too.
Here is a link to a starting point for Inkscape's API:
http://wiki.inkscape.org/wiki/index.php/Script_extensions
It looks like you can script within Inkscape, or access Inkscape via external scripts.
You also may be able to do something with zero scripting, from the inkscape command line interface:
http://wiki.inkscape.org/wiki/index.php/Frequently_asked_questions#Can_Inkscape_be_used_from_the_command_line.3F
COREL DRAW (App Link)
Corel Draw is recognized as the premier industry solution for vector graphics, and has some great tools for converting rasterized images into vector images.
Here's a link to their API:
https://community.coreldraw.com/sdk/api
Here's a link to Corel Draw batch image processing (non-script solution):
http://howto.corel.com/en/c/Automating_tasks_and_batch-processing_images_in_Corel_PHOTO-PAINT
I have generated set of points, that create polygonal areas border. On image below, there is an example of what I mean. The black "spots" should not be there and line should be "clear". I need to remove those points.
Now the problem is double. First, I dont know, how this situation is called. Its not aliasing or jagged edge, because those points are not obtained from line generating algorithm, but from contour generator.
And if not the name, than at least some push, how to solve this, would help me.
So far, I have tried convert this to chain code and simplify it, but that didn´t worked very well and it was rather slow. Convert those dots to geometry and use Ramer algorithm to simplify geometry works better, but it destroy some "fine" detail, that should be there.
You can try the following:
First search for these spots. From your figure it seems that the spots look something like the following:
1 1
1 1
That is, a square matrix of colored pixels. Such spots can easily be found by traversing the pixel matrix once.
Now once you identify these spots, you will need to check for the neighbouring pixels and see what pattern is the curve/line following and accordingly delete the unnecessary pixels.
Separate the contour curves and clean each one by itself.
For each contour:
If the curve is not closed, close it with a temporary line.
Flood-fill the contour curve to get a solid monochrome figure.
Run contour detection on the result. The edge of a monochrome figure will be a clean line.
Flood-fill the area outside the new contour curve.
Run contour detection one last time to restore the original contour.
Re-assemble the contours into a single bitmap.
I am writing a program in Matlab to detect a circle.
I've already managed to detect shapes such as the square, rectangle and the triangle, basically by searching for corners, and determining what shape it is based on the distance between them. The images are black and white, with black being the background and white the shape, so for me to find the corners I just have to search each pixel in the image until I find a white pixel.
However I just can't figure out how I can identify the circle.
Here it the an example of how a circle input would look like:
It is difficult to say what the best method is without more information: for example, whether more than one circle may be present, whether it is always centred in the image, and how resilient the algorithm needs to be to distortions. Also whether you need to determine the location and dimensions of the shape or simply a 'yes'/'no' output.
However a really simple approach, assuming only one circle is present, is as follows:
Scan the image from top to bottom until you find the first white pixel at (x1,y1)
Scan the image from bottom to top until you find the last white pixel at (x2,y2)
Derive the diameter of the suspected circle as y2 - y1
Derive the centre of the suspected circle as ((x1+x2)/2, y1+(y2-y1)/2)
Now you are able to score each pixel in the image as to whether it matches this hypothetical circle or not. For example, if a pixel is inside the suspected circle, score 0 if it is white and 1 if it black, and vice-versa if it is outside the suspected circle.
Sum the pixel scores. If the result is zero then the image contains a perfect circle. A higher score indicates an increasing level of distortion.
I think you may read about this two topics:
Theoretical:
Binary images
Hough transform
Matlab:
Circle Detection via Standard Hough Transform
Hough native in matlab
Binary images
Working on an android app, I have a bitmap obtained by applying edge detection on some image.
Black background bitmap with white lines as edges.
I need to identify the first closed boundary moving outward from the
centre and check if it is a triangle.
How do I do that? Even a methodology if not code sample would
be of much help.
This is modified Hough transform, a little optimized for this problem.
Assuming that you applied edge detection and edge is white pixel.
Find boundary. Move from center to outside and find first white pixel. Repeat for as many direction as you want.
Find lines. Route line through pixels that are neighbours (take two pixels or find equation to route line through more than two pixels) and check how many white pixels are under the line. The more pixel under line, the better line it is. Take into account intersection with another lines and count white pixels till the intersection.
Identify triangle. If boundary is builded from 3 good lines then it is a triangle.
It's only idea, I'll hope that help.