I am looking for a method that looks for shapes in 3D image in matlab. I don't have a real 3D sample image right now; in fact, my 3D image is actually a set of quantized 2D images.
The figure below is what I am trying to accomplish:
Although the example figure above is a 2D image, please understand that I am trying to do this in 3D. The input shape has these "tentacles", and I have to look for irregular shapes among them. The size of the tentacle from one point to another can change around but at "consistent and smooth" pace - that is it can be big at first, then gradually smaller later. But if suddenly, the shape just gets bigger not so gradually, like the red bottom right area in the figure above, then this is one of the volume of interests. Note that these shapes have more tendency to be rounded and spherical, but some of them are completely arbitrary and random.
I've tried the following methods so far:
Erode n times and dilate n times: given that the "tentacles" are always smaller than the volume of interest, this method will work as long as the volume is not too small. And, we need to have a mechanism to deal with thicker portion of the tentacle that becomes false positive somehow.
Hough Transform: although I have been suggested this method earlier (from Segmenting circle-like shapes out of Binary Image), I see that it works for some of the more rounded shape cases, but at the same time, more difficult cases such that of less-rounded, distorted, and/or arbitrary shapes can slip through this method.
Isosurface: because of my input is a set of 2D quantized images, using an isosurface allow me to reconstruct image in 3D and see things clearer. However, I'm not sure what could be done further in this case.
So can anyone suggests some other techniques for segmenting such shape out of these "tentacles"?
Every point on your image has the property that it is either part of the tentacle, or part of the volume of interest. If it is unknown apriori what the expected girth of the tentacle is, then 1 wont work because we won't be able to set n. However, we know that the n that erases the tentacle is smaller than the n that erases the node. You can for each point replace it with an integer representing the distance to the edge. Effectively, this can be done via successive single pixel erosion, and replacing each pixel with the count of the iteration at which it was erased. Lets call this the thickness at the pixel, but my rusty old mind tells me that there was a term of art for this.
Now we want to search for regions that have a higher-than-typical morphological distance from the boundary. I would do this by first skeletonizing the image (http://www.mathworks.com/help/toolbox/images/ref/bwmorph.html) and then searching for local maxima of the thickness along the skeleton. These are points on the skeleton where the thickness is larger than the neighbor points.
Finally I would sort the local maxima by the thickness, a threshold on which should help to separate the volumes of interest from the false positives.
Related
I am currently taking my first steps in the field of computer vision and image processing.
One of the tasks I'm working on is finding the center coordinates of (overlapping and occluded) circles.
Here is a sample image:
Here is another sample image showing two overlapping circles:
Further information about the problem:
Always a monochrome, grayscale image
Rather low resolution images
Radii of the circles are unknown
Number of circles in a given image is unknown
Center of circle is to be determined, preferably with sub-pixel accuracy
Radii do not have to be determined
Relative low overhead of the algorithm is of importance; the processing is supposed to be carried out with real-time camera images
For the first sample image, it is relatively easy to calculate the center of the circle by finding the center of mass. Unfortunately, this is not going to work for the second image.
Things I tried are mainly based on the Circle Hough Transform and the Distance Transform.
The Circle Hough Transform seemed relatively computationally expensive due to the fact that I have no information about the radii and the range of possible radii is large. Furthermore, it seems hard to identify the (appropriate) pixels along the edge because of the low resolution of the image.
As for the Distance Transform, I have trouble identifying the centers of the circles and the fact that the image needs to be binarized implies a certain loss of information.
Now I am looking for viable alternatives to the aforementioned algorithms.
Some more sample images (images like the two samples above are extracted from images like the following):
Just thinking aloud to try and get the ball rolling for you... I would be thinking of a Blob, or Connected Component analysis to separate out your blobs.
Then I would start looking at each blob individually. First thing is to see how square the bounding box is for each blob. If it is pretty square AND the centroid of the blob is central within the square, then you have a single circle. If it is not square, or the centroid is not central, you have more than one circle.
Now I am going to start looking at where the white areas touch the edges of the bounding box for some clues as to where the centres are...
I want to construct a 3D cube in MATLAB. I know that the units of any 3D shape are voxels not pixels. Here is what I want to do,
First, I want to construct a cube with some given dimensions x, y, and z.
Second, according to what I understand from different image processing tutorials, this cube must consists of voxels (3D pixels). I want to give every voxel an initial color value, say gray.
Third, I want to access every voxel and change its color, but I want to distinguish the voxels that represent the faces of the cube from those that represent the internal region. I want to axis every voxel by its position x,y, z. At the end, we will end up with a cube that have different colors regions.
I've searched a lot but couldn't find a good way to implement that, but the code given here seems very close in regard to constructing the internal region of the cube,
http://www.mathworks.com/matlabcentral/fileexchange/3280-voxel
But it's not clear to me how it performs the process.
Can anyone tell me how to build such a cube in MATLAB?
Thanks.
You want to plot voxels! Good! Lets see how we can do this stuff.
First of all: yeah, the unit of 3D shapes may be voxels, but they don't need to be. You can plot an sphere in 3D without it being "blocky", thus you dont need to describe it in term of voxels, the same way you don't need to describe a sinusoidal wave in term of pixels to be able to plot it on screen. Look at the figure below. (same happens for cubes)
If you are interested in drawing voxels, I generally would recommend you to use vol3D v2 from Matlab's FEX. Why that instead of your own?
Because the best (only?) way of plotting voxels is actually plotting flat square surfaces, 6 for each cube (see answer here for function that does that). This flat surfaces will also create some artifacts for something called z-fighting in computer graphics. vol3D actually only plots 3 surfaces, the ones looking at you, saving half of the computational time, and avoiding ugly plotting artifacts. It is easy to use, you can define colors per voxel and also the alpha (transparency) of each of them, allowing you to see inside.
Example of use:
% numbers are arbitrary
cube=zeros(11,11,11);
cube(3:9,3:9,3:9)=5; % Create a cube inside the region
% Boring: faces of the cube are a different color.
cube(3:9,3:9,3)=2;
cube(3:9,3:9,9)=2;
cube(3:9,3,3:9)=2;
cube(3:9,9,3:9)=2;
cube(3,3:9,3:9)=2;
cube(9,3:9,3:9)=2;
vold3d('Cdata',cube,'alpha',cube/5)
But yeah, that still looks bad. Because if you want to see the inside, voxel plotting is not the best option. Alphas of different faces stack one on top of the other and the only way of solving this is writing advanced computer graphics ray tracing algorithms, and trust me, that's a long and tough road to take.
Very often one has 4D data, thus data that contains 3D location and a single data for each of the locations. One may think that in this case, you really want voxels, as each of them have a 3D +color, 4D data. Indeed! you can do it with voxels, but sometimes its better to describe it in some other ways. As an example, lets see this person who wanted to highlight a region in his/hers 4D space (link). To see a bigger list I suggest you look at my answer in here about 4D visualization techniques.
Lets try wits a different approach than the voxel one. Lets use the previous cube and create isosurfaces whenever the 4D data changes of value.
iso1=isosurface(cube,1);
iso2=isosurface(cube,4);
p1=patch(iso1,'facecolor','r','facealpha',0.3,'linestyle','none');
p2=patch(iso2,'facecolor','g','facealpha',1,'linestyle','none');
% below here is code for it to look "fancy"
isonormals(cube,p1)
view(3);
axis tight
axis equal
axis off
camlight
lighting gouraud
And this one looks way better, in my opinion.
Choose freely and good plotting!
I want to extract orientations of strongly unclosed edges from a binary image. The image consists of blobs, blob rows and unsharp edges as shown below. In the end every pixel should be assigned to an information about the orientation of the edge. If the existence of an edge is not confident the point should not be assigned. Parameters of a line or a whole curve would be fine but are not necessarily needed. The edges to be found are marked as red curves:
I tried a lot and I hope for some hints in regarding to methods I could use.
Hough Transformation with Lines: Because of the existence of curves as well as point clouds it is difficult to extract the relevant extreme values of the HT.
Hough Transformation with Ellipses: Same disadvantages as ‘HT with Lines’. Plus the amount of curves and point arrangements to be detected exceeds the limits of a fast process.
Local masks: Go from pixel to pixel and estimate the orientation with the help of a directed mask (Example: Count all white pixels for every considered direction and make a decision in regarding to the highest number of found pixels). By using this method the view on bigger structures like whole blob rows is obscured. It is easy to see that this method will fail in clouds an edge goes through.
I guess an estimation of the orientation by considering local and global information is the only way. I need to know something about the connectivity of these blobs before making local decisions.
Btw, I am using MATLAB.
What about using image moments? you can calculate the angle, mayor axis, and eccentricity of each single blob and define parameters to merge interceeding ones.
You can use the regionprops() or start from scratch with this code I just so happend to have here:
function M=ImMoment(Image,ii,jj)
ImSize=size(Image);
M=0;
for k=1:ImSize(1);
for l=1:ImSize(2);
M=M+k^ii*l^jj*Image(k,l);
end
end
end
and for the covariance matrix:
function [Matrix,Centroid,Angle,Len,Wid,Eccentricity]=CovMat(Image)
Centroid=[ImMoment(Image,0,1)/ImMoment(Image,0,0),...
ImMoment(Image,1,0)/ImMoment(Image,0,0)];
Miu20=ImMoment(Image,0,2)/ImMoment(Image,0,0)-Centroid(1)^2;
Miu02=ImMoment(Image,2,0)/ImMoment(Image,0,0)-Centroid(2)^2;
Miu11=ImMoment(Image,1,1)/ImMoment(Image,0,0)-Centroid(1)*Centroid(2);
Matrix=[Miu20,Miu11
Miu11,Miu02];
Lambda1=(Miu20+Miu02)/2+sqrt(4*Miu11^2+(Miu20-Miu02)^2)/2;
Lambda2=(Miu20+Miu02)/2-sqrt(4*Miu11^2+(Miu20-Miu02)^2)/2;
Angle=1/2*atand(2*Miu11/(Miu20-Miu02));
Len=4*sqrt(max(Lambda1,Lambda2));
Wid=4*sqrt(min(Lambda1,Lambda2));
Eccentricity=sqrt(1-Lambda2/Lambda1);
end
Play a little bit around with that, I'm pretty sure that should work.
I am writing a matlab code that takes in a photo and detects the circular object. For example, the function takes a picture of a peach (circular object) as an input and will return the same image with the peach circled.
Currently, I am using hough transform, utilizing imfindcircles function. However, this function requires me to specify radius range and some sort of sensitivity/threshold value. These values differ for different sizes of image and round objects. So, to get the desired output, I will have to manually change these values for each input image, which is not what I want. I'm going to use this function on 100+ images, so it's impossible for me to do this manually.
My question is is there any way I can make my circular object detection function less manual and possibly completely automatic (does not require me to input any values, just the image)?
Complexity of circle detection
The Hough transform is a voting procedure that requires assumptions be made about the minimum and maximum radii of your circles. Generally speaking using the Randomized Hough Transform for Circles you would pick three-points and then try to form a circle and check if the radius is within the desired range. Running this for a good number of iterations you should find peaks (multiple hits) in your accumulator matrix that represent circles. If you didn't make any assumptions about object size I think it is obvious this method wouldn't work.
Do some routine pre-processing to adjust for contrast and brightness e.g. contrast stretching, histogram equalization. If you might have some noise in the images, then apply bit of gaussian smoothing as well.
Normalizing images this way will reduce inter-image variance and help you with setting thresholds.
the Hough Transform can be used to detect circles, lines, etc.You can refer the demos in Matlab. There are several cases for the application of Hough Transform.
I have a binary image, i want to detect/trace curves in that image. I don't know any thing (coordinates, angle etc). Can any one guide me how should i start? suppose i have this image
I want to separate out curves and other lines. I am only interested in curved lines and their parameters. I want to store information of curves (in array) to use afterward.
It really depends on what you mean by "curve".
If you want to simply identify each discrete collection of pixels as a "curve", you could use a connected-components algorithm. Each component would correspond to a collection of pixels. You could then apply some test to determine linearity or some other feature of the component.
If you're looking for straight lines, circular curves, or any other parametric curve you could use the Hough transform to detect the elements from the image.
The best approach is really going to depend on which curves you're looking for, and what information you need about the curves.
reference links:
Circular Hough Transform Demo
A Brief Description of the Application of the Hough
Transform for Detecting Circles in Computer Images
A method for detection of circular arcs based on the Hough transform
Google goodness
Since you already seem to have a good binary image, it might be easiest to just separate the different connected components of the image and then calculate their parameters.
First, you can do the separation by scanning through the image, and when you encounter a black pixel you can apply a standard flood-fill algorithm to find out all the pixels in your shape. If you have matlab image toolbox, you can find use bwconncomp and bwselect procedures for this. If your shapes are not fully connected, you might apply a morphological closing operation to your image to connect the shapes.
After you have segmented out the different shapes, you can filter out the curves by testing how much they deviate from a line. You can do this simply by picking up the endpoints of the curve, and calculating how far the other points are from the line defined by the endpoints. If this value exceeds some maximum, you have a curve instead of a line.
Another approach would be to measure the ratio of the distance of the endpoints and length of the object. This ratio would be near 1 for lines and larger for curves and wiggly shapes.
If your images have angles, which you wish to separate from curves, you might inspect the directional gradient of your curves. Segment the shape, pick set of equidistant points from it and for each point, calculate the angle to the previous point and to the next point. If the difference of the angle is too high, you do not have a smooth curve, but some angled shape.
Possible difficulties in implementation include thick lines, which you can solve by skeleton transformation. For matlab implementation of skeleton and finding curve endpoints, see matlab image processing toolkit documentation
1) Read a book on Image Analysis
2) Scan for a black pixel, when found look for neighbouring pixels that are also black, store their location then make them white. This gets the points in one object and removes it from the image. Just keep repeating this till there are no remaining black pixels.
If you want to separate the curves from the straight lines try line fitting and then getting the coefficient of correlation. Similar algorithms are available for curves and the correlation tells you the closeness of the point to the idealised shape.
There is also another solution possible with the use of chain codes.
Understanding Freeman chain codes for OCR
The chain code basically assigns a value between 1-8(or 0 to 7) for each pixel saying at which pixel location in a 8-connected neighbourhood does your connected predecessor lie. Thus like mention in Hackworths suggestions one performs connected component labeling and then calculates the chain codes for each component curve. Look at the distribution and the gradient of the chain codes, one can distinguish easily between lines and curves. The problem with the method though is when we have osciallating curves, in which case the gradient is less useful and one depends on the clustering of the chain codes!
Im no computer vision expert, but i think that you could detect lines/curves in binary images relatively easy using some basic edge-detection algorithms (e.g. sobel filter).