Shape Analysis - Science topic

Aastha Aastha One basic thing that hasn't been mentioned is that a 2-fold change in diameter is an 8-fold change in mass or volume. (Another way of looking at this is that a 1% change in diameter produces a 3% change in volume - or 2% in surface/projected area). However, one imagines that the mass of the particle doesn't/cannot change and thus the density must reduce (with incorporation of water) in the swelling process as the volume is obviously increasing.

With imaging you're looking at a 2-D representation of a 3-D particle. All of these things need consideration. What is the increase you're trying to document? Length, surface, volume?

The manual is quite clear, but it gives (almost) for granted the user be familiar with the physical principles of laser vibrometry. In my case, I had to use the rotational laser vibrometer from Polytec to measure shaft torsional vibrations. Although the rotational speed was measured correctly, i had big doubts that the angular velocity vibration was captured correctly. The signal appeared harmonically distorted and had huge "runout" components that, as far as i know, should have not been there. I tried to compensate for this runout by taking samples at low speed, but didn´t go too far. I believe if the surfaces are not prepared in a perfect, lab-style way, you might end up facing similar issue. The distance, the material and the light conditions do seem to play a relevant part, but for that i think it´s wise sticking to the user´s manual.

It's a classic case use for ARIMA, a regression method that allows accounting for repeated measurements along time. You can find insights here:

Thanks a lot Dr. Miriam Leah Zelditch

But, i still have a problem, .NTS file, that have been got with function (operation) make sliders file on tpsutil, can't be opened on tpsrelw (number of columns not a multiple of dimensions). Before do that, i have made file from function append tps curve to landmark on tpsutil succesfully, and that file can be opened on tpsrelw.

Dear Dimitri,

I suggest you to explore the Morpho R package. Once you import an array, you can run the function procSym setting the argument sizeshape on TRUE (the log of CS is added to the coordinates after GPA). Another function you may be interested is the CAC (common allommetric component). Anyway, my suggestion is to explore the Form space (procSym function scale=FALSE, CSInit=FALSE).

Best,

AP

Agnishwar Girigoswami

Yes, microscopy is essential but may not be quantitative and we often have a low contrast image for the materials that are described. Usually though we only have a 2D image of a 3 particle and 'sample preparation' (especially TEM) is a trap for the unwary. Cryo-TEM has had excellent success.

In OpenCV, that was only for 2D planar polygons and more focused on polygonal approximation (Douglas-Peucker algorithm) than corner detection. Unless you had a more specific implementation in mind fulfilling the requirements I carefully explained in my main question?

As for Matlab, my implementation needs to be integrated into a C++ application so not very helpful (as explained in the question).

Regards

Dear Salah,

welcome,

I do not see no scatter of y versus x. Scattering means for the same X there will be multiple points centered around an average value. Here you need only to interpolate your points to find the values between the original points. There curve fitting tool books in matlab that you can use them.

Best wishes

This is an interesting topic in deep learning, with the typical question: ‘Now I’ve created (generative adversarial networks) or modified (super resolution or de-noising) an image how close is it to the true image or gold standard?’ There are many methods for evaluating images: Structural Similarity Index (SSIM), Peak Signal to Noise Ratio (PSNR), Mean Squared Error (MSE), Visual Information Fidelity (VIF), Universal Quality Index (UQI), Perceptual Image Patch Similarity (LPIPS) and Frechet Inception distance (FID). Though these metrics could not be counted upon solely as reference for human judgement of image quality (Armanious et al. 2019).

Armanious, et al. (2019). MedGAN: Medical Image Translation using GANs. Downloaded on 2019061x from: https://arxiv.org/abs/1806.06397

Heusel, et al. (2017). GANs trained by a two time-scale update rule converge to a nash equilibrium. arXiv preprint arXiv:1706.08500 .

Zhang, et al. (2018). The Unreasonable Effectiveness of Deep Features as a Perceptual Metric. https://arxiv.org/abs/1801.03924v2

Two interesting sources discussing evaluating 3D images:

Taha & Hanbury (2015). Metrics for evaluating 3D medical image segmentation: analysis, selection, and tool. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4533825/

Murphy (2011). Development and Evaluation of 2D and 3D Image Quality Metrics.

Hope this helps.

This is a good and very tricky question. I am tempted to say that humans are inherently metric in their perception of reality. Just imagine a hunter 10000 years ago estimating the distance to the pray and trying to use the right amount of strenth to throw a spear. But then, I see the work of a potter usind clay and I have to accept that he may have some (at least intuitive) topological knowledge acquired by mere practice.

Friend, it depends on the problem and the type of image. for example, analyzing a pulmonary nodule can be done by texture and shape. Then it is necessary to analyze if the image is x-ray or computed tomography. Perhaps the techniques used for one case do not suit another case.

If you specify your problem better, it may be easier to suggest a technique.

Use TEM for size and shap

Aparna Sathya Murthy : A shape is fixed by three point in 3D. In terms of translations and rotations, you can think of it this way. If point A maps to A', that takes care of three translations, but the shape can freely rotate attached to A'. If a second point B maps to B', the shape can only rotate around line A'B'. A third point C' fixates that last degree of freedom.

Chin Fung Tsang : If there are deformations, we are not talking about linear transformations anymore; the "degrees of freedom" (if that term still makes sense) might be infinite. The number of points needed depends on the accuracy you want. There is no general recipe.

It is all about the shape aberration from the circle, isn't it?

If you can discretize the image to triangular mesh, determine the distance range between the closest and the most distant vertices from the pore barycenter. Calculate weighted average distance between the barycenter and every vertex in that ring. Sum all distances between the neighbouring vertices in the ring and divide with the circumference of weighted mean distance from the barycenter. What you get is a dimensionless positive real number that tells you how many times is the rim of that pore longer than rim of the circle with the radius you calculated as weighted average distance.

If you can't triangulate the image you must work with the intensity values from the image. A circular pore has small area of the transitional intensity gradient in the edge region. A complex pore must have greater area in the same region. If you divide the first one with the second one and take the square root out of it, you should get the ratio analogue to the mesh based solution.

In both solution you should figure out how to compensate for inaccuracy due to discretization.

As per my knowledge HOG with LBP is better solution for obtaining good result.

This is a good question. From shapes and sizes of living things in nature, I will add behaviors as well, why they behave differently according to seasons, is survival and continuity in existence. As most of you pointed out, for instance the shape and sizes of trees in desert areas (tiny in an optimal way) are clearly indicative of a purpose driven natural process to optimize resources of water beneath and survive in the desert. For the actual sequential processes, the Fibonacci sequence is one vital process in which branches of brocolis, cabbages and others multiply. These acts and process are purely mathematical and the very reason we say nature is mathematical. Galileo here is a right person to mention, "The universe can not be read until we know its language in which things are written, which is mathematics"

Your question is challenging from a design point of view.

A simple construction that could help you was to look at the unit normal vector (the direction) to the shape at every point on the shape contour. This I hope will be invariant  to translation and scaling but assuming that you have a registration between the two shapes you can find the rotation by taking an average of the angles between the unit normal vectors at all points.

This method will breakdown for the shapes with rotational symmetry but I do not know whether you would be able to distinguish them easily with some other descriptors.

In a recent paper ("The Gradient Product Transform for Symmetry Detection and Blood Vessel Extraction", VISAPP 2015), I have used the DRIVE database (“Digital Retinal Images for Vessel Extraction”) (Staal et al., 2004) to test a skeleton extraction algorithm.

It contains Retina images and manually labeled ground truth blood vessels (no skeletons, but with some thickness). Maybe you can use it somehow.

Hello

You look at this web site

or at this again

or

Cordially

Dear Jose Pablo Suarez, 

Look the link. May be useful.

Regards, Shafagat

there are no specific shape extraction algorithms as such. but you can use edge detection techniques for finding the edges and depending the specific shape you want, you should write the logic in MATLAB. of course there are inbuilt shape detection algorithms in MATLAB, for example, you can detect the circle shapes in MATLAB 2013 using the following code:

I = imread('coins.png'); % read the image

hautoth = vision.Autothresholder;

BW = step(hautoth, I); % threshold the image

[y, x]= find(BW,1); % select a starting point for the trace

% Determine the boundaries

hboundtrace = vision.BoundaryTracer;

PTS = step(hboundtrace, BW, [x y]);

% Display the results

figure, imshow(BW);

hold on; plot(PTS(:,1), PTS(:,2), 'r', 'Linewidth',2);

hold on; plot(x,y,'gx','Linewidth',2); % show the starting point.

the result you get is:

file attached .

thank you sir.

These two operations have different goals, inputs and outputs.

Thresholding: Works from grayscale images to separate "intelligently" pixels into 2 populations (black and white) by finding a specific gray value as a threshold.

Labeling: Works from an already segmented image (as obtained from thresholding) and assigns a unique label to each isolated components. It is therefore not a segmentation method. These components can later be analyzed individually by other image processing algorithms.

I suggest you look at any general book on image processing to see visual examples of these techniques and common implementation methods.  If you are doing C or C++, OpenCV is a great place to look for robust and high performance implementations of MANY computer vision algorithms. Otherwise, Matlab, Maple or Mathematica all have interactive environments where you can play with these algorithms.

Hi Prasad,

Here is what I came up using MIPAR. It's a lengthy recipe, but nicely separates the exudates from the OD. I chose to start from the original image (actually the green channel of it), so as to use only MIPAR-available tools, but we will be adding the Fuzzy C-means algorithm soon, and I think applying that prior the other recipe steps will make the segmentation even easier. 

I have attached:

Let me know if you have any questions. The sky's the limit with MIPAR, so I am confident we could come up with a different recipe given your needs.

Cheers,

John

I am sorry that my researchgate account was associated with an discontinued email, so I didn't receive any notifications on new updates. 

@Mehran I ended up using distance metrics such as mean absolute distance (you need to setup a kd tree) and Euler characteristic. The following is the resulting publication. 

Ukwatta, Eranga, et al. "Image-based reconstruction of three-dimensional myocardial infarct geometry for patient-specific modeling of cardiac electrophysiology." Medical physics 42.8 (2015): 4579-4590.

Fourier shape analysis is quite common in fisheries studies where fish can be classified into groups by the shape of the otolith (ear bone). Momocs is a really neat package in R for this and the user guide should give you some good ideas on how to start.

regards,

james 

The answer lies in the synthesis process itself. For eg synthesis using conventional solid state route may introduce a temperature gradient which will effect sintered surface and hence particle size and shapes. Similar observations could be observed by changing the ball to powder ratio during ball milling and so on. Similarly you could think about the process used by you or if you find it appropriate I suggest sharing the process and material details so that experts in the field could provide better explanation. Hope this will help. 

There are two curvatures at each point of a smooth surface, the mean and the gaussian curvatures. You can classify surfaces according to them because they are invariants for free surfaces in space. Here you have a reference where this is used.

You can try the wire electrical discharge machining.

Dear Sumukh,

Have alook at:http://alice.loria.fr/publications/papers/2006/SMI_Laplacian/SMI_Laplacian.pdf

Best wishes,

Abel

Uhm, if C is not diagonally dominant, then the mapping should be by some other method (and then two objects are very dissimilar...).

  If you mean matrix C is diagonally dominant, although it is not diagonal, then that is the usual case with functional maps. 

Maybe you tell us more about your intended application?

Digital curves can be detected using the so-called Generalized Hough Transform. Regarding chain code, each curve pixel is represented by a number (0,1,...8) indicating its orientation with respect to its preceding pixel. Differential chain code is invariant to image rotation.

Hi Mer,

if you say kinetic data from a VT experiment do you mean exchange data. Is this from a liquids sample. In this case DNMR is better than sola.  DNMR is described in the DNMR manual. For help on SOLA check chapter 6 of the structur analysis tools manual. Both manuals can be found under Help (?), Manuals, Analysis and Simulation.

Clemens

Dear Alese Wooditch,

Thanks for your answer. I will follow this.

This is a  good question with lots of possible answers.

An approach to shape matching with the Smith Waterman algorithm using Matlab is given in

C. Wang, A. Stefanidis, A. Croitoru, P. Agouris, Map registration of image sequences using linear features, Photogrammetric Engineering & Remote Sensing 74, 2008, no. 4, 25-38:

See Appendix 1, page 38, pseudocode for an implementation of the modified Smith Waterman algorithm.

More to the point, consider

L. Hasan, Hardware Acceleration of Bioinformatics, Ph.D. thesis, TU Delft, 2011.

See the detailed flow chart for implementation of the Smith Waterman algorithm in Appendix D, starting on page 123   See, especially, Figure D.1 on page 124.

You need to convert your shapefile into parcel fabric with the following steps

The most critical ones is converting your polygon into parcel fabric (step 1 - 5). If the step 6 has error, that means the topology has error.

I made a tutorial, however it is in Indonesian. You may use googletranslate to get the points. 

you are in the segmentation and pattern recognition domain. Many softwares and documentation are available. An overview on segmentation approaches and technics is necessary to take a good way according to the input data in query.

In the classical snake, the internal energy is divided into two parts:

- The first derivative, which tries to maintain the points equally spread along the curve.

 - The second derivative, which tries to keep all the points in a straight line.

This means that if you have a closed curve and no other energy, the points will tend to shrink until collapse in an unique point. I am not sure whether this is your problem, but if it is you need to add other energies, since the internal only smooth the curve. When employing snakes for segmentation is common to use the gradient to adapt the contours to the image contours. Another options are the mumford-shah functional or mixing different features. For instance, if you have a vertebra in CT, finding the point that maximizes a mixture of the gradient and the intensity may help to get the real vertebral shape. 

Hope it helps.

Hi Sherief,

you should use the function "Identify primary objects".

The function is quite complex but in essence does the following:

-Separates background (no cells) from foreground, by intensity threshold

-tries to separate touching cells in foreground by watershed methods

Start with finding a good intensity threshold. first manual, if this doesnt work try the automatic global ones. if they do not work, try the adaptive ones. 

Next, try to find best parameters for objects separation. A bit of background reading, what a watershed does, will be helpful.

Best

Christoph

For researchers interested in otoliths morphometries is interesting to know AFORO website (http://aforo.cmima.csic.es), an interactive open system to deal with shape analysis of fish otoliths and a classification system based on the mathematical properties of the one-dimensional curves describing the Teleostean otolith contours. The system was created in 2003 and connected a website with a database of complete morphometric (measures and morphological indexes) information, including Elliptic Fourier analysis and wavelets (WT) based in otolith contours of the otolith images of well identified samples. Since 2006, AFORO incorporates an expert system that will allow carrying automatic taxon identification based. In 2009 AFORO was included in GBIF (Global Biodiversity Information facility) databases system, with geographical information of the otolith samples. The AFORO database and public web site (the otolith guide, with its corresponding shape analysis and classification system) keep continuously implemented. At present AFORO includes 4555 images of different specimen from 1381 species, from 216 families, and 36 orders worldwide represented. Nevertheless, Mediterranean Sea is the best represented area (90% of common species, 64% of species sometimes cited in this area, including 50% of Lessepsian species -Red Sea invaders- are showed). The main advance in the last years was the inclusion of videos of 3D otolith objects in 2012, obtained with LED white light-based scanner, which eliminates the speckle noise effect of laser scanners. and the inclusion of automatic morphometric software and numerical information of Fourier and wavelet analysis, which will be used as morphometric bank for researchers that requires precise species identification as paleontologist, archeologist and trophic ecologist.

Dear aneesh how many parmeters, which can express in numerical value, do you have?

When you break symmetry, you also break the degeneracy that causes certain peaks to overlap. For example, in a cubic crystal the d spacings associated with (100), (010), and (001) planes (that is, the a, b, and c lattice parameters) are all the same, but in a tetragonal distortion one would be slightly different from the other two. So, for example, what used to be a single {100} peak becomes two peaks. One is actually the (100) and (010) peaks superposed, and the other is the (001). If your sample is untextured, those two peaks would have a 2:1 intensity ratio. You need sufficient XRD resolution to separate those two peaks. Then you just figure out the d spacings and you're basically done. To check your answer you can calculate the d spacings where you should see all the other peaks you're finding in your measurement.

Now, that said, a lot of crystals have their {100} reflections forbidden by symmetry. You may need to perform a similar trick on {200} or some other peak, depending on your material.

For a more robust analysis, you should curve fit the whole thing using Rietveld refinement. There are lots of software packages out there for that.

Yep, We used LBP feature for OCR in Birjand competition and we gained the first place position.

Finding the spines could be done just by "skeletonizing" (process > binary > skeletonize) the binary image and searching the ending points of the line. There are some problems with the noise and outliers points on the initial image, so probably the number of spines found will be overstimated (see image). Anyway, this could be solved in a later step.

Once the spines are located, some questions arise: how the diameter is defined? and the length?

Dear Umar,

Can I have your segmentation code???

They are not always same! Centroid obtained from edge image will be more biased to the smoothness of its boundary. Consider a circular shape where left half of its boundary is smooth and right half is rough. Lets consider the number of boundary pixels in right side is two times than that is in left. In this scenario, centroid from the edge image will be detected further right than it is detected from the segmented mask.

Hi David,

you should check out the publications from Peter Claes from the Biomedical Imaging group of ESAT in KULeuven. They do all kinds of 3D surface map morphometrics of facial scans, but also other stuff. We are currently apply their technique on bony plates of seahorses, and plan to do the same on facial scans of European eels in the future.

Some references:

Baynam, G., Walters, M., Claes, P., Le Souef, P., 2012. 3D facial analysis can investigate vaccine responses. Med Hypotheses. 78, 497-501.

Claes, P., Walters, M., Clement, J., 2012. Improved facial outcome assessment using a 3D anthropometric mask. Int J Oral Max Surg. 41, 324-330.

Claes, P., Walters, M., Vandermeulen, D., Clement, J.G., 2011. Spatially-dense 3D facial asymmetry assessment in both typical and disordered growth. J Anat. 219, 444-455.

Claes, P., Vandermeulen, D., De Greef, S., Willems, G., Clement, J.G., Suetens, P., 2010. Computerized craniofacial reconstruction: Conceptual framework and review. Forensic Sci Int. 201, 138-145.

Claes, P., Daniels, K., Walters, M., Clement, J., Vandermeulen, D., Suetens, P., 2012. Dysmorphometrics: the modelling of morphological abnormalities. Theor Biol Med Model. 9.

Claes, P., Walters, M., Shriver, M.D., Puts, D., Gibson, G., Clement, J., Baynam, G., Verbeke, G., Vandermeulen, D., Suetens, P., 2012. Sexual dimorphism in multiple aspects of 3D facial symmetry and asymmetry defined by spatially dense geometric morphometrics. Journal of Anatomy. 221, 97-114.

Vandermeulen, D., Claes, P., Loeckx, D., De Greef, S., Willems, G., Suetens, P., 2006. Computerized craniofacial reconstruction using CT-derived implicit surface representations. Forensic Sci Int. 159, S164-S174.

best

Dominique

Dear Gerrit,

I do not know where is freeware for the mentioned problem computation.

At the same time, I propose that our paper published in 2000 in not very popular Journal "Scientific Israel" may clear some peculiarities of this process. You can download this article at the ResearchGate.

Aleinikov, A.L., Belikov, V.T., Eppelbaum, L.V. and Nemzorov, N.I., 2000. Mountainous rock destruction and metamorphic processes in the Earth: A view from classical physics. Scientific Israel, No.3, 65-87.

Hi Mahsa.

Shape description is a very useful tool in many field of computer vision like OCR,Object detection and tracking,Face detection,facial expression ,etc .

your question located on the special topic of computer vision named: " Shape analysis"

We have 2 main topic in this field:

1- fixed shape analysis and matching

2- deformable shape analysis and matching

--First Group--

If you have template of your desire object you can assist temple matching methods in fixed shape matching group. also GHT (Generalized Hough Transform) which located in this group can help you to model and detect arbitrary object.

--Second Group--

This group consist of 4 main topic:

1- Deformable templates

2- Active contours and snakes

3- Shape skeletonization

4- Active shape models

Each methods have advantage and disadvantages and each of them are appropriate for specific application.

Also, many implementation and sample code available for these methods.

If you need more information don't hesitate to contact me.

Ioannis' response is correct. If you want the transformation to be defined everywhere and for this ordering preservation to hold for every pair of curves then you must have a combination of an isometry or global scaling. In other words, your only options are translation, scaling and rotation. Such transformations are generally called "similarity transforms", since they would also map polygons to similar polygons. Specific tools for computing these are available in many image registration toolkits, including ITK.

The second option you describe is unfortunately kind of hard to formalize. In particular, taking means over an infinite dimensional space of paths has its complications. However, if you are looking for a "softened" deformation model without such a harsh constraint as the finite-dimensional similarity transforms, then there are many useful models that use metrics with interpretations that sound similar to this. In particular the diffeomorphic image registration algorithms used in computational anatomy and medical image analysis would be of interest (search terms: LDDMM, b-splines, demons).

Hope this is of some use.