I've developed a little program that let me load an image then make some angle measurements onto it. Here is a screenshot (there is no image loaded in this screenshot).
When all the measurements are done I have a list of x, y and angle values. What I'd like to do is interpolate them to generate some kind of graph.
I would prefer to directly implement this functionality and not rely on any other library (as long as it's possible and not to complicated).
So basically I see two steps, first interpolating the data, second, generating a graph from it.
At first I was going to implement some bicubic interpolation but this kind of interpolation needs a regular grid, which I can't ensure.
For the moment I think I have to main options:
Convert my data to a regular grid and then do a bicubic interpolation.
Find an other kind of interpolation that doesn't require a regular grid.
What way do you think I should go and do you have any idea of which grid-redefining/interpolation I should use? I don't have any opinion on both methods but I think this is going to take me a lot of time and I wouldn't like to realize in the end that I am in a dead-end.
If this is of any relevance I'm working with Qt and on windows.
Edit: Basically I want something like that in the end:
What you are looking for is a 2D Least squares fitting function, and generating a heat map or a 3D surface.
QWT is nice library that can help with graphing it, but it is doable without it.
Google Least Squares 2D Calculation
Related
I have a 3D image data obtained from a 3D OCT scan. The data can be represented as I(x,y,z) which means there is an intensity value at each voxel.
I am writing an algorithm which involves finding the image's gradient in x,y and z directions in C++. I've already written a code in C++ using OpenCV for 2D and want to extend it to 3D with minimal changes in my existing code for 2D.
I am familiar with 2D gradients using Sobel or Scharr operators. My search brought me to this post, answers to which recommend ITK and Point Cloud Library. However, these libraries have a lot more functionalities which might not be required. Since I am not very experienced with C++, these libraries require a bit of reading, which time doesn't permit me. Moreover, these libraries don't use cv::Mat object. If I use anything other than cv::Mat, my whole code might have to be changed.
Can anyone help me with this please?
Update 1: Possible solution using kernel separability
Based on #Photon's answer, I'm updating the question.
From what #Photon says, I get an idea of how to construct a Sobel kernel in 3D. However, even if I construct a 3x3x3 cube, how to implement it in OpenCV? The convolution operations in OpenCV using filter2d are only for 2D.
There can be one way. Since the Sobel kernel is separable, it means that we can break the 3D convolution into convolution in lower dimensions. Comments 20 and 21 of this link also tell the same thing. Now, we can separate the 3D kernel but even then filter2D cannot be used since the image is still in 3D. Is there a way to break down the image as well? There is an interesting post which hints at something like this. Any further ideas on this?
Since the Sobel operator is separable, it's easy to envision how to add a 3rd dimension.
For example, when you look at the filter definition for Gx in the link you posted, you see that is multiplies the surrounding pixels by coefficients that have a sign dependent on the relative X position, and magnitude relative to the offset in Y.
When you extend to 3D, the Gx gradient should be calculated the same way, but you need to work on a 3x3x3 cube, and the coefficient sign remains the same definition, and the magnitude now depends on change in either Y or Z or both.
The other gradients (Gy, Gz) are the same but around their axis.
To give you an idea of where I'm coming from, this started as a teaching exercise to get a 12-year-old video game addict into coding. The 2D games, I did in SDL with him and that was fine because I wasn't planning on going into 3D. Yeah, right! So now I'm in at the deep end in OpenGL and mainly trying to figure out exactly what it can and cannot do. I understand the theory (still working on beziers and nurbs if the truth be told) and could code the whole thing by hand in calculated triangular vertices but I'd hate to spend days on that only to be told that there's a built in function/library that does the whole thing faster and easier.
Quadrics seem to be extremely powerful but not terribly flexible. Consider the human head - roughly speaking a 3x4x3 sphere or a torso as a truncated cone that's taller than it is wide than it is thick. Again, a quadric shape with independent x,y and z radii. Since only one radius is provided, am I right in thinking that I would have to generate it around the origin and then apply a scaling matrix to adjust them? Furthermore, if this is so, am I also correct in thinking that saving the results into a vertex array rather than a frame list results in the system neither knowing or caring how they got there?
Transitions: I'm familiar with the basic transitions but, again, consider the torso. It can achieve, maybe, a 45 degree twist from the hips to the shoulders that is distributed linearly across the entire length or even the sideways lean. This is applied around the Y or Z axis respectively but I've obviously missed something about applying transformations that are based on an independent value. (eg rot = dist x (max_rot/max_dist). Again, I could do this by hand (and will probably have to in order to apply the correct physics) but does OpenGL have this functionality built in somewhere?
Any other areas of research I need to put in would be appreciated in the notes.
I am writing an application in C++ that requires a little bit of image processing. Since I am completely new to this field I don't quite know where to begin.
Basically I have an image that contains a rectangle with several boxes. What I want is to be able to isolate that rectangle (x, y, width, height) as well as get the center coordinates of each of the boxes inside (18 total).
I was thinking of using a simple for-loop to loop through the pixels in the image until I find a pattern but I was wondering if there is a more efficient approach. I also want to see if I can do it efficiently without using big libraries like OpenCV.
Here are a couple example images, any help would be appreciated:
Also, what are some good resources where I could learn more about image processing like this.
The detection algorithm here can be fairly simple. Your box-of-squares (BOS) is always aligned with the edge of the image, and has a simple structure. Here's how I'd approach it.
Choose a colorspace. Assume RGB is OK for now, but it may work better in something else.
For each line
For each pixel, calculate the magnitude difference between the pixel and the pixel immediately below it. The magnitude difference is simply sqrt((X-x)^2+(Y-y)^2+(Z-z)^2)), where X,Y,Z are color coordinates of the first pixel, and x,y,z are color coordinates of the pixel below it. For RGB, XYZ=RGB of course.
Calculate the maximum run length of consecutive difference magnitudes that are below a certain threshold magThresh. You may also choose a forgiving version of this: maximum run length, but allowing intrusions up to intrLen pixels long that must be followed by up to contLen pixels long runs. This is to take care of possible line-to-line differences at the edges of the squares.
Find the largest set of consecutive lines that have the maximum run lengths above minWidth and below maxWidth.
Thus you've found the lines which contain the box, and by recalculating data in 2.1 above, you'll get to know where the boxes are in horizontal coordinates.
Detecting box edges is done by repeating the same thing but scanning left-to-right within the box. At that point you'll have approximate box centroids that take no notice of bleeding between pixels.
This can be all accomplished by repeatedly running the image through various convolution kernels followed by doing thresholding, I'd think. The good thing is that both of those operations have very fast library implementations. You do not want to reimplement them by hand, it will be likely significantly slower.
If you insist on doing it yourself (personally I'd use OpenCV, it's industrial-strength and free), you're going to need an edge detection algorithm first. There are a good few out there on the internet, but be prepared for some frightening mathematics...
Many involve iterating over each pixel, and lifting it and it's neighbours' values into a matrix, and then convolving with a kernel matrix. Be aware that this has to be done for every pixel (in principle though, in your case you can stop at the first discovered rectangle), and for each colour channel - so it would be highly advisable to push onto the GPU.
I have a path made up of a list of 2D points. I want to turn these into a strip of triangles in order to render a textured line with a specified thickness (and other such things). So essentially the list of 2D points need to become a list of vertices specifying the outline of a polygon that if rendered would render the line. The problem is handling the corner joins, miters, caps etc. The resulting polygon needs to be "perfect" in the sense of no overdraw, clean joins, etc. so that it could feasibly be extruded or otherwise toyed with.
Are there any simple resources around that can provide algorithm insight, code or any more information on doing this efficiently?
I absolutely DO NOT want a full fledged 2D vector library (cairo, antigrain, OpenVG, etc.) with curves, arcs, dashes and all the bells and whistles. I've been digging in multiple source trees for OpenVG implementations and other things to find some insight, but it's all terribly convoluted.
I'm definitely willing to code it myself, but there are many degenerate cases (small segments + thick widths + sharp corners) that create all kinds of join issues. Even a little help would save me hours of trying to deal with them all.
EDIT: Here's an example of one of those degenerate cases that causes ugliness if you were simply to go from vertex to vertex. Red is the original path. The orange blocks are rectangles drawn at a specified width aligned and centered on each segment.
Oh well - I've tried to solve that problem myself. I wasted two month on a solution that tried to solve the zero overdraw problem. As you've already found out you can't deal with all degenerated cases and have zero overdraw at the same time.
You can however use a hybrid approach:
Write yourself a routine that checks if the joins can be constructed from simple geometry without problems. To do so you have to check the join-angle, the width of the line and the length of the joined line-segments (line-segments that are shorter than their width are a PITA). With some heuristics you should be able to sort out all the trivial cases.
I don't know how your average line-data looks like, but in my case more than 90% of the wide lines had no degenerated cases.
For all other lines:
You've most probably already found out that if you tolerate overdraw, generating the geometry is a lot easier. Do so, and let a polygon CSG algorithm and a tesselation algorithm do the hard job.
I've evaluated most of the available tesselation packages, and I ended up with the GLU tesselator. It was fast, robust, never crashed (unlike most other algorithms). It was free and the license allowed me to include it in a commercial program. The quality and speed of the tesselation is okay. You will not get delaunay triangulation quality, but since you just need the triangles for rendering that's not a problem.
Since I disliked the tesselator API I lifted the tesselation code from the free SGI OpenGL reference implementation, rewrote the entire front-end and added memory pools to get the number of allocations down. It took two days to do this, but it was well worth it (like factor five performance improvement). The solution ended up in a commercial OpenVG implementation btw :-)
If you're rendering with OpenGL on a PC, you may want to move the tesselation/CSG-job from the CPU to the GPU and use stencil-buffer or z-buffer tricks to remove the overdraw. That's a lot easier and may be even faster than CPU tesselation.
I just found this amazing work:
http://www.codeproject.com/Articles/226569/Drawing-polylines-by-tessellation
It seems to do exactly what you want, and its licence allows to use it even in commercial applications. Plus, the author did a truly great job to detail his method. I'll probably give it a shot at some point to replace my own not-nearly-as-perfect implementation.
A simple method off the top of my head.
Bisect the angle of each 2d Vertex, this will create a nice miter line. Then move along that line, both inward and outward, the amount of your "thickness" (or thickness divided by two?), you now have your inner and outer polygon points. Move to the next point, repeat the same process, building your new polygon points along the way. Then apply a triangualtion to get your render-ready vertexes.
I ended up having to get my hands dirty and write a small ribbonizer to solve a similar problem.
For me the issue was that I wanted fat lines in OpenGL that did not have the kinds of artifacts that I was seeing with OpenGL on the iPhone. After looking at various solutions; bezier curves and the like - I decided it was probably easiest to just make my own. There are a couple of different approaches.
One approach is to find the angle of intersection between two segments and then move along that intersection line a certain distance away from the surface and treat that as a ribbon vertex. I tried that and it did not look intuitive; the ribbon width would vary.
Another approach is to actually compute a normal to the surface of the line segments and use that to compute the ideal ribbon edge for that segment and to do actual intersection tests between ribbon segments. This worked well except that for sharp corners the ribbon line segment intersections were too far away ( if the inter-segment angle approached 180' ).
I worked around the sharp angle issue with two approaches. The Paul Bourke line intersection algorithm ( which I used in an unoptimized way ) suggested detecting if the intersection was inside of the segments. Since both segments are identical I only needed to test one of the segments for intersection. I could then arbitrate how to resolve this; either by fudging a best point between the two ends or by putting on an end cap - both approaches look good - the end cap approach may throw off the polygon front/back facing ordering for opengl.
See http://paulbourke.net/geometry/lineline2d/
See my source code here : https://gist.github.com/1474156
I'm interested in this too, since I want to perfect my mapping application's (Kosmos) drawing of roads. One workaround I used is to draw the polyline twice, once with a thicker line and once with a thinner, with a different color. But this is not really a polygon, it's just a quick way of simulating one. See some samples here: http://wiki.openstreetmap.org/wiki/Kosmos_Rendering_Help#Rendering_Options
I'm not sure if this is what you need.
I think I'd reach for a tessellation algorithm. It's true that in most case where these are used the aim is to reduce the number of vertexes to optimise rendering, but in your case you could parameterise to retain all the detail - and the possibility of optimising may come in useful.
There are numerous tessellation algorithms and code around on the web - I wrapped up a pure C on in a DLL a few years back for use with a Delphi landscape renderer, and they are not an uncommon subject for advanced graphics coding tutorials and the like.
See if Delaunay triangulation can help.
In my case I could afford to overdraw. I just drow circles with radius = width/2 centered on each of the polyline's vertices.
Artifacts are masked this way, and it is very easy to implement, if you can live with "rounded" corners and some overdrawing.
From your image it looks like that you are drawing box around line segments with FILL on and using orange color. Doing so is going to create bad overdraws for sure. So first thing to do would be not render black border and fill color can be opaque.
Why can't you use GL_LINES primitive to do what you intent to do? You can specify width, filtering, smoothness, texture anything. You can render all vertices using glDrawArrays(). I know this is not something you have in mind but as you are focusing on 2D drawing, this might be easier approach. (search for Textured lines etc.)
I am currently working on a data visualization project.My aim is to produce contour lines ,in other words iso-lines, from gridded data.Data can be temperature, weather data or any kind of other environmental parameters but only condition is it must be regularly spaced.
I searched in internet , however i could not find a good algorithm, pseudo-code or source code for producing contour lines from grids.
Does anybody knows a library, source code or an algorithm for producing contour lines from gridded data?
it will be good if your suggestion has a good run time performance, i don't want to wait my users so much :)
Edit: thanks for response but isolines have some constrains like they should not intersects
so just generating bezier curves does not accomplish my goal.
See this question: How to approximate a vector contour from an elevation raster?
It's a near duplicate, but uses quite different terminology. You'll find that cartography and computer graphics solve many of the same problems, but use different terminology for them.
there's some reasonably good contouring available in GNUplot - if you're able to use GPL code that may help.
If your data is placed at regular intervals, this can be done fairly easily (assuming I understand your problem correctly). First you need to determine at what interval you want your contours. Next create the grid you are going to use to store the contour information (i'm assuming just a simple on/off or elevation at this contour level type of data), which should be one interval smaller than the source data.
Now the trick here is to offset the 2 grids by 1/2 an interval (won't actually show up in code like this, but its the concept I'm dealing with here) and compare the 4 coordinates surrounding the current point in the contour data grid you are calculating. If any of the 4 points are in a different interval range, then that 'pixel' in the contour grid should be set to true (or the value of the contour range being crossed).
With this method, there will be a problem when the interval is too fine which will cause several contours to overlap onto each other.
As the link from Paul Tomblin suggests, Bezier curves (which are a subset of B-splines) are a ripe solution for your problem. If runtime performance is an issue, Bezier curves have the added benefit of being constructable via the very fast de Casteljau algorithm, instead of drawing them according to the parametric equations. On the off chance you're working with DirectX, it has a library function for the de Casteljau, but it should not be challenging to brew one yourself using the 1001 web pages that describe it.