I have a time series of trajectories with X,Y coordinates, with a known start and finish. And I need a change point detection algorithm able to detect changes in the "curve" of each series (one algorithm for all series and future ones that may come). The problem is that the curves are quite different between them, nevertheless most of the time a human eye can easly spot the change point.
The CPD should be bases in the curve, so not mean nor variance. I have tried creating a basic regression + cost minimitzation algoithm with poor results. I am using python. Any ideas of algorithms/libraries I could use?
An example of the data:
The green cross is the change point.
1:
Related
I'm trying to understand the paper : https://netman.aiops.org/wp-content/uploads/2018/05/PID5338621.pdf about Robust and Rapid Clustering of KPIs for Large-Scale Anomaly Detection.
Clustering is done using ROCKA algorithm.
Steps:
1.) Preprocessing is conducted on the raw KPI data to remove amplitude differences and standardize data.
2.) In baseline extraction step, we reduce noises, remove the extreme values (which are likely anomalies), and extract underlying shapes, referred to as baselines, of KPIs. It's done by applying moving average with a small sliding window.
3.) Clustering is then conducted on the baselines of sampled KPIs, with robustness against phase shifts and noises.
4.) Finally, we calculate the centroid of each cluster, then assign the unlabeled KPIs by their distances to these centroids.
I understand ROCKA mechanism.
Now, i'm trying to understand DONUT algorithm which is applied for "Anomaly Detection".
How it works is :
DONUT applies sliding windows over the KPI to get short series x and tries to recognize what normal patterns x follows. The indicator is then calculated by the difference between reconstructed normal patterns and x to show the severity of anomalies. In practice, a threshold should be selected for each KPI. A data point with an indicator value larger than the threshold is regarded as an anomaly.
Now my question is :
IT seems like DONUT is not robust enough against time information related anomalies. Meaning that it works on a set of sliding windows and it ignores the relationship between windows. So the window becomes a very critical parameter here. So it might generate high false positives. What I'm understanding wrong here?
Please help and make me understand how DONUT will capture the relationship between sliding windows.
I have set of 2000 plane images similar to image below. Plane has different angle on every image. Image size is 512x512 and in every image is always this same plane.
My goal is to find angle on image which is not in test set.
So far I tried:
Harris corner detection, but in every image Harris gives me differnt
amount of points, event for images with very similar position.
Hough Lines Transform to find the longest line and get inclination to the axis X.
Corelation - this method gives the best results, but it take really long time and angels are only rough.
Neural network
Back porpagation to train image from Harris points and hough lines transform, but without any success.
I so 3D object in STP file, but I have no idea how to use it, to solve my problem.
It would be nice to get any sugestion of method, article or example.
In my experience, a convolutional neural network (CNN) will help you a great deal here. The performance will be great at detecting angles.
But here is the problem, depending of how you define the output to be and the number of layers (no more than three should be enough), the training can be very costly. For example, you could have one single output that could give you a real number which indicates the angle. Training this should be costly, but it is normal in CNNs. However, if you say you want to have 360 outputs (one for each angle in a 360 degree system), in that case the training will be a very painful and unpleasant long experience; the performance could be better, but not significantly.
(I wanted to write this as a comment to your question first, but I don't have enough reputation to do that yet, sorry.)
I've been working on a project for some time, to detect and track (moving) vehicles in video captured from UAV's, currently I am using an SVM trained on bag-of-feature representations of local features extracted from vehicle and background images. I am then using a sliding window detection approach to try and localise vehicles in the images, which I would then like to track. The problem is that this approach is far to slow and my detector isn't as reliable as I would like so I'm getting quite a few false positives.
So I have been considering attempting to segment the cars from the background to find the approximate position so to reduce the search space before applying my classifier, but I am not sure how to go about this, and was hoping someone could help?
Additionally, I have been reading about motion segmentation with layers, using optical flow to segment the frame by flow model, does anyone have any experience with this method, if so could you offer some input to as whether you think this method would be applicable for my problem.
Below is two frames from a sample video
frame 0:
frame 5:
Assumimg your cars are moving, you could try to estimate the ground plane (road).
You may get a descent ground plane estimate by extracting features (SURF rather than SIFT, for speed), matching them over frame pairs, and solving for a homography using RANSAC, since plane in 3d moves according to a homography between two camera frames.
Once you have your ground plane you can identify the cars by looking at clusters of pixels that don't move according to the estimated homography.
A more sophisticated approach would be to do Structure from Motion on the terrain. This only presupposes that it is rigid, and not that it it planar.
Update
I was wondering if you could expand on how you would go about looking for clusters of pixels that don't move according to the estimated homography?
Sure. Say I and K are two video frames and H is the homography mapping features in I to features in K. First you warp I onto K according to H, i.e. you compute the warped image Iw as Iw( [x y]' )=I( inv(H)[x y]' ) (roughly Matlab notation). Then you look at the squared or absolute difference image Diff=(Iw-K)*(Iw-K). Image content that moves according to the homography H should give small differences (assuming constant illumination and exposure between the images). Image content that violates H such as moving cars should stand out.
For clustering high-error pixel groups in Diff I would start with simple thresholding ("every pixel difference in Diff larger than X is relevant", maybe using an adaptive threshold). The thresholded image can be cleaned up with morphological operations (dilation, erosion) and clustered with connected components. This may be too simplistic, but its easy to implement for a first try, and it should be fast. For something more fancy look at Clustering in Wikipedia. A 2D Gaussian Mixture Model may be interesting; when you initialize it with the detection result from the previous frame it should be pretty fast.
I did a little experiment with the two frames you provided, and I have to say I am somewhat surprised myself how well it works. :-) Left image: Difference (color coded) between the two frames you posted. Right image: Difference between the frames after matching them with a homography. The remaining differences clearly are the moving cars, and they are sufficiently strong for simple thresholding.
Thinking of the approach you currently use, it may be intersting combining it with my proposal:
You could try to learn and classify the cars in the difference image D instead of the original image. This would amount to learning what a car motion pattern looks like rather than what a car looks like, which could be more reliable.
You could get rid of the expensive window search and run the classifier only on regions of D with sufficiently high value.
Some additional remarks:
In theory, the cars should even stand out if they are not moving since they are not flat, but given your distance to the scene and camera resolution this effect may be too subtle.
You can replace the feature extraction / matching part of my proposal with Optical Flow, if you like. This amounts to identifying flow vectors that "stick out" from a consistent frame-to-frame motion of the ground. It may be prone to outliers in the optical flow, however. You can also try to get the homography from the flow vectors.
This is important: Regardless of which method you use, once you have found cars in one frame you should use this information to robustify your search of these cars in consecutive frame, giving a higher likelyhood to detections close to the old ones (Kalman filter, etc). That's what tracking is all about!
If the number of cars in your field of view always remain the same but move around then you can use optical flow...it will give you good results against a still background...if the number of cars are changing then you need to call goodFeaturestoTrack function in OpenCV after certain number of frames and again track the cars using optical flow.
You can use background modelling to model the background and hence the cars are always your foreground.The simplest example is frame differentiation...subtract the previous frame current frame. diff(x,y,k) = I(x,y,k) - I(x,y,k-1) .As your cars are moving in each frame you will get their position..
Both the process will work fine since you have a still background I presume..check this link to find what Optical flow can do.
I am working on HOG descriptors and I am pretty much done with most of the parts, except the fusion of the detection windows.
What I have done so far is; I build a scale space pyramid of the image and for each image on each scale I move the detection window(64x128) and detect humans. In each image a person is detected by more than one window.
So the question is how to fuse all these windows(assume for one person) into one window. Dalal suggests that one should use a robust mod detection algorithm, such as mean-shift. But, I have multiple scales... Should I first estimate the true location of the detection window found in lower levels of the scale space in order to do that?
Any help is appreciated.
Thanks in advance.
My interpretation is that mean shift would give you in effect what you are suggesting.
Essentially, you estimate the probability distribution of the location of the person at the coarsest scale first based upon the strengths of the detector outputs. This gives you a robust estimate of mode.
You can then iteratively refine using the finer scales around the maximum or the mode.
The idea is very similar that used in pyramidal LK tracking, for example. You can also do ensemble processing and/or particle filters.
I have a field filled with obstacles, I know where they are located, and I know the robot's position. Using a path-finding algorithm, I calculate a path for the robot to follow.
Now my problem is, I am guiding the robot from grid to grid but this creates a not-so-smooth motion. I start at A, turn the nose to point B, move straight until I reach point B, rinse and repeat until the final point is reached.
So my question is: What kind of techniques are used for navigating in such an environment so that I get a smooth motion?
The robot has two wheels and two motors. I change the direction of the motor by turning the motors in reverse.
EDIT: I can vary the speed of the motors basically the robot is an arduino plus ardumoto, I can supply values between 0-255 to the motors on either direction.
You need feedback linearization for a differentially driven robot. This document explains it in Section 2.2. I've included relevant portions below:
The simulated robot required for the
project is a differential drive robot
with a bounded velocity. Since
the differential drive robots are
nonholonomic, the students are encouraged to use feedback linearization to
convert the kinematic control output
from their algorithms to control the
differential drive robots. The
transformation follows:
where v, ω, x, y are the linear,
angular, and kinematic velocities. L
is an offset length proportional to the
wheel base dimension of the robot.
One control algorithm I've had pretty good results with is pure pursuit. Basically, the robot attempts to move to a point along the path a fixed distance ahead of the robot. So as the robot moves along the path, the look ahead point also advances. The algorithm compensates for non-holonomic constraints by modeling possible paths as arcs.
Larger look ahead distances will create smoother movement. However, larger look ahead distances will cause the robot to cut corners, which may collide with obstacles. You can fix this problem by implementing ideas from a reactive control algorithm called Vector Field Histogram (VFH). VFH basically pushes the robot away from close walls. While this normally uses a range finding sensor of some sort, you can extrapolate the relative locations of the obstacles since you know the robot pose and the obstacle locations.
My initial thoughts on this(I'm at work so can't spend too much time):
It depends how tight you want or need your corners to be (which would depend on how much distance your path finder gives you from the obstacles)
Given the width of the robot you can calculate the turning radius given the speeds for each wheel. Assuming you want to go as fast as possible and that skidding isn't an issue, you will always keep the outside wheel at 255 and reduce the inside wheel down to the speed that gives you the required turning radius.
Given the angle for any particular turn on your path and the turning radius that you will use, you can work out the distance from that node where you will slow down the inside wheel.
An optimization approach is a very general way to handle this.
Use your calculated path as input to a generic non-linear optimization algorithm (your choice!) with a cost function made up of closeness of the answer trajectory to the input trajectory as well as adherence to non-holonomic constraints, and any other constraints you want to enforce (e.g. staying away from the obstacles). The optimization algorithm can also be initialised with a trajectory constructed from the original trajectory.
Marc Toussaint's robotics course notes are a good source for this type of approach. See in particular lecture 7:
http://userpage.fu-berlin.de/mtoussai/teaching/10-robotics/