please i like to classify a set of image in 4 class with SIFT DESCRIPTOR and SVM. Now, using SIFT extractor I get keypoints of different sizes exemple img1 have 100 keypoints img2 have 55 keypoints.... how build histograms that give fixed size vectors with matlab
In this case, perhaps dense sift is a good choice.
There are two main stages:
Stage 1: Creating a codebook.
Divide the input image into a set of sub-images.
Apply sift on each sub-image. Each key point will have 128 dimensional feature vector.
Encode these vectors to create a codebook by simply applying k-means clustering with a chosen k. Each image will produce a matrix Vi (i <= n and n is the number of images used to create the codeword.) of size 128 * m, where m is the number of key points gathered from the image. The input to K-means is therefore, a big matrix V created by horizontal concatenation of Vi, for all i. The output of K-means is a matrix C with size 128 * k.
Stage 2: Calculating Histograms.
For each image in the dataset, do the following:
Create a histogram vector h of size k and initialize it to zeros.
Apply dense sift as in step 2 in stage 1.
For each key point's vector find the index of it's "best match" vector in the codebook matrix C (can be the minimum in the Euclidian distance) .
Increase the corresponding bin to this index in h by 1.
Normalize h by L1 or L2 norms.
Now h is ready for classification.
Another possibility is to use Fisher's vector instead of a codebook, https://hal.inria.fr/file/index/docid/633013/filename/jegou_aggregate.pdf
You will always get different number of keypoints for different images, but the size of feature vector of each descriptor point remains same i.e. 128. People prefer using Vector Quantization or K-Mean Clustering and build Bag-of-Words model histogram. You can have a look at this thread.
Using the conventional SIFT approach you will never have the same number of key points in every image. One way of achieving that is to sample the descriptors densely, using Dense SIFT, that places a regular grid on top of the image. If all images have the same size, then you will have the same number of key points per image.
Related
Apologies for the overlap with existing questions; mine is at a more basic skill level. I am working with very sparse occurrences spanning very large areas, so I would like to calculate probability at pixels using the density.ppp function (as opposed to relrisk.ppp, where specifying presences+absences would be computationally intractable). Is there a straightforward way to convert density (intensity) to probabilities at each point?
Maxdist=50
dtruncauchy=function(x,L=60) L/(diff(atan(c(-1,1)*Maxdist/L)) * (L^2 + x^2))
dispersfun=function(x,y) dtruncauchy(sqrt(x^2+y^2))
n=1e3; PPP=ppp(1:n,1:n, c(1,n),c(1,n), marks=rep(1,n));
density.ppp(PPP,cutoff=Maxdist,kernel=dispersfun,at="points",leaveoneout=FALSE) #convert to probabilies?
Thank you!!
I think there is a misunderstanding about fundamentals. The spatstat package is designed mainly for analysing "mapped point patterns", datasets which record the locations where events occurred or things were located. It is designed for "presence-only" data, not "presence/absence" data (with some exceptions).
The relrisk function expects input data about the presence of two different types of events, such as the mapped locations of trees belonging to two different species, and then estimates the spatially-varying probability that a tree will belong to each species.
If you have 'presence-only' data stored in a point pattern object X of class "ppp", then density(X, ....) will produce a pixel image of the spatially-varying intensity (expected number of points per unit area). For example if the spatial coordinates were expressed in metres, then the intensity values are "points per square metre". If you want to calculate the probability of presence in each pixel (i.e. for each pixel, the probability that there is at least one presence point in the pixel), you just need to multiply the intensity value by the area of one pixel, which gives the expected number of points in the pixel. If pixels are small (the usual case) then the presence probability is just equal to this value. For physically larger pixels the probability is 1 - exp(-m) where m is the expected number of points.
Example:
X <- redwood
D <- density(X, 0.2)
pixarea <- with(D, xstep * ystep)
M <- pixarea * D
p <- 1 - exp(-M)
then M and p are images which should be almost equal, and can both be interpreted as probability of presence.
For more information see Chapter 6 of the spatstat book.
If, instead, you had a pixel image of presence/absence data, with pixel values equal to 1 or 0 for presence or absence respectively, then you can just use the function blur in the spatstat package to perform kernel smoothing of the image, and the resulting pixel values are presence probabilities.
I'm trying to develop a fully-convolutional neural net to estimate the 2D locations of keypoints in images that contain renders of known 3D models. I've read plenty of literature on this subject (human pose estimation, model based estimation, graph networks for occluded objects with known structure) but no method I've seen thus far allows for estimating an arbitrary number of keypoints of different classes in an image. Every method I've seen is trained to output k heatmaps for k keypoint classes, with one keypoint per heatmap. In my case, I'd like to regress k heatmaps for k keypoint classes, with an arbitrary number of (non-overlapping) points per heatmap.
In this toy example, the network would output heatmaps around each visible location of an upper vertex for each shape. The cubes have 4 vertices on top, the extruded pentagons have 2, and the pyramids just have 1. Sometimes points are offscreen or occluded, and I don't wish to output heatmaps for occluded points.
The architecture is a 6-6 layer Unet (as in this paper https://arxiv.org/pdf/1804.09534.pdf). The ground truth heatmaps are normal distributions centered around each keypoint. When training the network with a batch size of 5 and l2 loss, the network learns to never make an estimate whatsoever, just outputting blank images. Datatypes are converted properly and normalized from 0 to 1 for input and 0 to 255 for output. I'm not sure how to solve this, are there any red flags with my general approach? I'll post code if there's no clear problem in general...
Example:
Given n number of images marked 1 to n where n is unknown, I can calculate a property of every image which is a scalar quantity. Now I have to represent this property of all images in a fixed size vector (say 5 or 10).
One naive approach can be this vector- [avg max min std_deviation]
And I also want to include the effect of relative positions of those images.
What your are looking for is called feature extraction.
There are many techniques for the same, for images:
For your purpose try:
PCA
Auto-encoders
Convolutional Auto-encoders, 1 & 2
You could also look into conventional (old) methods like SIFT, HOG, Edge Detection, but they all will need an extra step for making them to a smaller-fixed size.
I've a small set of data points (around 10) in a 2D space, and each of them have a category label. I wish to classify a new data point based on the existing data point labels and also associate a 'probability' for belonging to any particular label class.
Is it appropriate to label the new point based on the label to its nearest neighbor( like a K-nearest neighbor, K=1)? For getting the probability I wish to permute all the labels and calculate all the minimum distance of the unknown point and the rest and finding the fraction of cases where the minimum distance is lesser or equal to the distance that was used to label it.
Thanks
The Nearest Neighbour method is already using the Bayes theorem to estimate the probability using the points in a ball containing your chosen K points. There is no need to transform, as the number of points in the ball of K points belonging to each label divided by the total number of points in that ball already is an approximation of the posterior probability of that label. In other words:
P(label|z) = P(z|label)P(label) / P(z) = K(label)/K
This is obtained using the Bayes rule of probability on an estimated probability estimated using a subset of the data. In particular, using:
VP(x) = K/N (this gives you the probability of a point in a ball of volume V)
P(x) = K/NV (from above)
P(x=label) = K(label)/N(label)V (where K(label) and N(label) are the number of points in the ball of that given class and the number of points in the total samples of that class)
and
P(label) = N(label)/N.
Therefore, just pick a K, calculate the distances, count the points and by checking their labels and recounting you will have your probability.
Roweis uses a probabilistic framework with KNN in his publication Neighbourhood Component Analysis. The idea is to use a "soft" nearest neighbour classification, where the probability that a point i uses another point j as its neighbour is defined by
,
where d_ij is the euclidean distance between point i and j.
The are no probabilities for such K-nearest classification method because it is discriminative classification as well as SVM. There are should be used postporcess for learning probabilities on unseen data with generative model like logistic regression.
1. learn K nearest classifier
2. Train logistic regression on distance and average distance to K nearest for validation data.
Check for details LibSVM article.
Sort the distances to the 10 centres; they could be
1 5 6 ... — one near, others far
1 1 1 5 6 ... — 3 near, others far
... lots of possibilities.
You could combine the 10 distances to a single number, e.g. 1 - (nearest / average) ** p,
but that's throwing away information.
(Different powers p makes the hills around the centres steeper or flatter.)
If your centres are really Gaussian hills though, take a look at
Multivariate kernel density estimation.
Added:
There are zillions of functions that go smoothly between 0 and 1,
but that doesn't make them probabilities of something.
"Probability" means either that chance, likelihood, is involved,
as in probability of rain;
or that you're trying to impress somebody.
Added again: scholar.google.com "(single|1) nearest neighbor classifier" gets > 300 hits;
"k nearest neighbor classifier" gets almost 3000.
It seems to me (non-expert) that, out of 10 different ways of mapping k-NN distances to labels,
each one might be better than the 9 others — for some data, with some error measure.
Anyway, you could try asking stats.stackexchange.com ,
The answer is : it depends.
Imagine your labels are the surname of a person, and the X,Y coordinates represent some essential characteristics of the person's DNA sequence. Clearly a more close DNA description enhance the probability of having the same surnames.
Now suppose the X,Y is the lat/long of the work office for that person. Working closer isn't related to label (surname) sharing.
So, it depends on the semantic of your tags and axes.
HTH!
I am playing with some models for the game glest.
These models are made up of one or more meshes; each mesh is made up of many frames which describe the position of each vertex for each frame of animation. In the model shown below, the position of each vertex in each wheel in each frame is in an array.
These models have been exported from 3D tools like Blender. Someone somewhere has the originals.
But I am wondering, for simple animation such as a wheel turning, how can you compute the transforms - the steps of rotate, scale and translate, or the matrix that when applied to the previous frame will result in the new frame?
(Obviously not all frames will have such transforms, because they may distort the models and such.)
Also, how can you detect mirroring and other opportunities to reduce the amount of vertex data by applying a matrix and rendering the same vertices again?
Running speed - if its measured in just minutes - won't be a problem.
First off, some assumptions:
You're dealing with 3D affine transformations (linear transformation plus translation).
You have the vertices for each frame in your animation
You can associate at least 4 vertices in a frame with 4 vertices in the next frame
Then you can take 4 vertices as 4D collumn vectors (appending a 1 in each vector's 4th element) in the original space and concatenate them to create a 4x4 matrix, called X. Do the same for their corresponding vectors in the tranformed space and call them Y, which will also be a 4x4 matrix. A little linear algebra provides you with a method to find the 4x4 matrix A that when applied to X gives you Y. Thus:
AX = Y
A = YX-1
Using this to get rotations and scaling is not trivial. However, the rightmost column of A will contain the translation for the object between the successive frames.