I notice that resonance audio envelope the listener by HOA, I am curious about how do you deal with forbiden frequency (non-uniqueness) in HOA?
HOA describes sound fields accurately only up to a certain frequency and only within a limited region. This is because the spherical Bessel functions only vanish for small wavenumber * radius values. For higher values, indeed, they can be null and the sound field reconstruction will suffer from spatial aliasing errors.
To deal with this problem, I think it is a common practice to apply frequency-dependent smoothing functions in the spherical harmonics domain. For example, instead of trying to reconstruct a high-frequency sound field, we can apply 'MaxRe' weighting factors to form a different kind of an ambisonic 'panner', which will assure best energy concentration in the direction of the virtual source.
Related
I am comparing models for the detection of objects for maritime Search and Rescue (SAR) purposes. From the models that I used, I got the best results for the improved version of YOLOv3 for small object detection and for FASTER RCNN.
For YOLOv3 I got the best mAP#50, but for FASTER RCNN I got better all other metrics (precision, recall, F1 score). Now I am wondering how to read it and which model is really better in this case?
I would like to add that there are only two classes in the dataset: small and large objects. We chose this solution because the objects' distinction between classes is not as important to us as the detection of any human origin object.
However, small objects don't mean small GT bounding boxes. These are objects that actually have a small area - less than 2 square meters (e.g. people, buoys). Large objects are objects with a larger area (boats, ships, canoes, etc.).
Here are the results per category:
And two sample images from the dataset (with YOLOv3 detections):
The mAP for object detection is the average of the AP calculated for all the classes. mAP#0.5 means that it is the mAP calculated at IOU threshold 0.5.
The general definition for the Average Precision(AP) is finding the area under the precision-recall curve.
The process of plotting the model's precision and recall as a function of the model’s confidence threshold is the precision recall curve.
Precision measures how accurate is your predictions. i.e. the percentage of your predictions that are correct. Recall measures how good you find all the positives. F1 score is HM (Harmonic Mean) of precision and recall.
To answer your questions now.
How to read it and which model is really better in this case?
The mAP is a good measure of the sensitivity of the neural network. So good mAP indicates a model that's stable and consistent across difference confidence thresholds. In your case faster rcnn results indicate that precision-recall curve metric is bad compared to that of Yolov3, which means that either faster rcnn has very bad recall at higher confidence thresholds or very bad precision at lower confidence threshold compared to that of Yolov3 (especially for small objects).
Precision, Recall and F1 score are computed for given confidence threshold. I'm assuming you're running the model with default confidence threshold (could be 0.25). So higher Precision, Recall and F1 score of faster rcnn indicate that at that confidence threshold it's better in terms of all the 3 metric compared to that of Yolov3.
What metric should be more important?
In general to analyse better performing model, I would suggest you to use validation set (data set that is used to tune hyper-parameters) and test set (data set that is used to assess the performance of a fully-trained model).
Note: FP - False Positive FN - False Negative
On validation set:
Use mAP to select best performing model (model that is more stable and consistent) out of all the trained weights across iterations/epochs. Use mAP to understand whether model should be trained/tuned further or not.
Check class level AP values to ensure model is stable and good across the classes.
As per use-case/application, if you're completely tolerant to FNs and highly intolerant to FPs then to train/tune the model accordingly use Precision.
As per use-case/application, if you're completely tolerant to FPs and highly intolerant to FNs then to train/tune the model accordingly use Recall.
On test set:
If you're neutral towards FPs and FNs, then use F1 score to evaluate best performing model.
If FPs are not acceptable to you (without caring much about FNs) pick the model with higher Precision
If FNs are not acceptable to you (without caring much about FPs) pick the model with higher Recall
Once you decide metric you should be using, try out multiple confidence thresholds (say for example - 0.25, 0.35 and 0.5) for given model to understand for which confidence threshold value the metric you selected works in your favour and also to understand acceptable trade off ranges (say you want Precision of at least 80% and some decent Recall). Once confidence threshold is decided, you use it across different models to find out best performing model.
I've spent a few hours doing research on numeric integration and velocity/position estimation but I couldn't really find an answer that would be either understandable by my brain or appropriate for my situation.
I have an IMU (Inertial Measurement Unit) that has a gyro, an accelerometer and a magnetometer. All those sensors are in fusion, which means for example using the gyro I'm able to compensate for the gravity in the accelerometer readings and the magnetometer compensates the drift.
In other words, I can get pure acceleration readings using such setup.
Now, I'm trying to accurately estimate the position based on acceleration, which as you may know requires double integration, and there are various methods of doing that. But I don't know which would be the most appropriate here.
Could somebody please share some information about this?
Also, I'd appreciate it if you could explain it to me without using any complex math formulas/symbols, I'm not a mathematician and this was one of my problems when looking for information.
Thanks
You can integrate the accelerations by simply summing the acceleration vectors multiplied by the timestep (period of the IMU) to get the velocity, then sum the velocities times the timestep to get the position. You can propagate (not integrate) the orientation by using various methods depending on which orientation representation you choose (Euler angles, Quaternions, Attitude Matrix (DCM), Axis-Angle, etc..).
However you have a bigger problem.
Long story short: Unless you have a naval-quality IMU (USD$200,000+) you cannot simply integrate the accelerations and angular rates to get an accurate pose (position and orientation) estimates.
I assume you are using a low-cost (under USD$1,000) IMU - your accelerometer and gyro are subject to both noise and bias. These will make it impossible to get accurate pose by simply integrating.
In practice to do what you are intending it is required to fuse 'correcting' measurements of the position and optionally the orientation. The IMU 'predicts' the position/orientation, while another sensor model (camera features, gps, altimeter, range/bearing measurements) take the predicted position and 'correct' it. There are various methods of fusing this data, the most prolific of which is the Extended Kalman Filter or Error-State (Indirect) Kalman Filter.
Back to your original question; I would represent the orientation as quaternions, and you can propagate the quaternion orientation by using the error-quaternion derivative and the angular rates from your gyro.
EDIT:
The noise problem can be partially worked around by using a high pass
filter, but what kind of bias are you exactly talking about?
You should read up on the sources of error in MEMS accelerometers: constant alignment bias, random walk bias, white noise and temperature bias. As you said you can high-pass filter to reduce the effect of noise - however this is not perfect so there is significant residual noise. The double integration of the residual noise gives a quadratically-increasing position error. Even after removing the acceleration due to gravity there will be significant accelerations measured due to these error sources which will render the position estimate inaccurate within less than 1 second of integration.
Given a video with a fixed background containing a lot of variation in light I am trying to detect pulses of light that occur for relatively short spans of time. When the video is played it is pretty easy for a person to distinguish the light pulses but if only shown a still frame it would be impossible to distinguish a pulse from background light.
I would like to know if there is specific terminology in machine vision that I can use to search for algorithms used to solve this problem. Also if you have any references for papers or open source software that solves this problem that would be great.
Edit: More context
The video itself is of a biological process that occurs at the sub-cellular level and while the background is fixed there is also a significant amount of random signal noise at the pixel level (there doesn't appear to be significant correlation in the noise between neighboring pixels). Note that the variation I refer to in the first paragraph is true variation and not signal noise. Since I mentioned that the process is biological it's probably also worth saying that there is no movement going on; these are just pulses of light. Also, the pulses themselves occupy enough pixels so that it is easy to discern their relative sizes.
From statistics, you could look into change point detection. The essential idea being that most of the time each (x,y) point or region, if you define some granularity of regions, has an intensity I(x,y), where I(x,y) is random, but either bounded or stochastic with some assumed distribution (e.g. normal with a given mean and standard deviation), and then it is observed with an intensity that is anomalous for that distribution. Anomaly detection would also apply, but the time series nature is more appropriate.
(If you want to go more into the statistical methodologies, it would be far more appropriate to discuss this on the statistics Stack Exchange site.)
If you look into astronomical applications, you can find papers on supernova and pulsar detection.
Update 1. Just to clarify the astronomical analogies, if the pulse is repeating, then papers on pulsars or satellites may be most appropriate. If the pulse is one-time, then papers on supernova detection would be better. If the pulse is bursty, and spatially clustered, then meteor strike detection would be better. Although spatial time series analysis, especially change point or anomaly detection, is useful, it's best to have an understanding of the stochastic phenomena of interest in order to narrow down the detection methodology.
To continue the notion of applying statistics: you might consider gridding each image frame into rectangular neighborhoods. At each time t, compute the variance (or standard deviation) of the neighborhood. Presumably, the unexcited neighborhoods will exhibit some common distribution of intensity (i.e. uniform, but most likely some form of gaussian). The presence of pulse pixels will bias that distribution in some way. When comparing a neighborhood at time t and t-1, a significant change in mean intensity (or a change in the variance, etc.) would indicate an excited neighborhood.
You might also consider looking at other measures, such as skewness and kurtosis. Assuming the initial, unexcited distribution is gaussian, the "shape" parameters could also identify differences in the pixel populations.
*Note that I'm assuming a grayscale image for simplicity, but the same principles may be applied to an RGB image.
Assuming a completely static scene with no object and camera motion, then any color deviation would be due to lighting changes.
If you detect an abrupt color/intensity change at particular pixels (i.e. brighness change above a certain allowable threshold), then this should be due to the light source turning on/off.
If you are only interested in point light sources, then any change in a region larger than the maximum apparent light source should be considered as coming from something else (e.g. the sun suddenly revealed from behind clouds).
100 periods have been collected from a 3 dimensional periodic signal. The wavelength slightly varies. The noise of the wavelength follows Gaussian distribution with zero mean. A good estimate of the wavelength is known, that is not an issue here. The noise of the amplitude may not be Gaussian and may be contaminated with outliers.
How can I compute a single period that approximates 'best' all of the collected 100 periods?
Time-series, ARMA, ARIMA, Kalman Filter, autoregression and autocorrelation seem to be keywords here.
UPDATE 1: I have no idea how time-series models work. Are they prepared for varying wavelengths? Can they handle non-smooth true signals? If a time-series model is fitted, can I compute a 'best estimate' for a single period? How?
UPDATE 2: A related question is this. Speed is not an issue in my case. Processing is done off-line, after all periods have been collected.
Origin of the problem: I am measuring acceleration during human steps at 200 Hz. After that I am trying to double integrate the data to get the vertical displacement of the center of gravity. Of course the noise introduces a HUGE error when you integrate twice. I would like to exploit periodicity to reduce this noise. Here is a crude graph of the actual data (y: acceleration in g, x: time in second) of 6 steps corresponding to 3 periods (1 left and 1 right step is a period):
My interest is now purely theoretical, as http://jap.physiology.org/content/39/1/174.abstract gives a pretty good recipe what to do.
We have used wavelets for noise suppression with similar signal measured from cows during walking.
I'm don't think the noise is so much of a problem here and the biggest peaks represent actual changes in the acceleration during walking.
I suppose that the angle of the leg and thus accelerometer changes during your experiment and you need to account for that in order to calculate the distance i.e you need to know what is the orientation of the accelerometer in each time step. See e.g this technical note for one to account for angle.
If you need get accurate measures of the position the best solution would be to get an accelerometer with a magnetometer, which also measures orientation. Something like this should work: http://www.sparkfun.com/products/10321.
EDIT: I have looked into this a bit more in the last few days because a similar project is in my to do list as well... We have not used gyros in the past, but we are doing so in the next project.
The inaccuracy in the positioning doesn't come from the white noise, but from the inaccuracy and drift of the gyro. And the error then accumulates very quickly due to the double integration. Intersense has a product called Navshoe, that addresses this problem by zeroing the error after each step (see this paper). And this is a good introduction to inertial navigation.
Periodic signal without noise has the following property:
f(a) = f(a+k), where k is the wavelength.
Next bit of information that is needed is that your signal is composed of separate samples. Every bit of information you've collected are based on samples, which are values of f() function. From 100 samples, you can get the mean value:
1/n * sum(s_i), where i is in range [0..n-1] and n = 100.
This needs to be done for every dimension of your data. If you use 3d data, it will be applied 3 times. Result would be (x,y,z) points. You can find value of s_i from the periodic signal equation simply by doing
s_i(a).x = f(a+k*i).x
s_i(a).y = f(a+k*i).y
s_i(a).z = f(a+k*i).z
If the wavelength is not accurate, this will give you additional source of error or you'll need to adjust it to match the real wavelength of each period. Since
k*i = k+k+...+k
if the wavelength varies, you'll need to use
k_1+k_2+k_3+...+k_i
instead of k*i.
Unfortunately with errors in wavelength, there will be big problems keeping this k_1..k_i chain in sync with the actual data. You'd actually need to know how to regognize the starting position of each period from your actual data. Possibly need to mark them by hand.
Now, all the mean values you calculated would be functions like this:
m(a) :: R->(x,y,z)
Now this is a curve in 3d space. More complex error models will be left as an excersize for the reader.
If you have a copy of Curve Fitting Toolbox, localized regression might be a good choice.
Curve Fitting Toolbox supports both lowess and loess localized regression models for curve and curve fitting.
There is an option for robust localized regression
The following blog post shows how to use cross validation to estimate an optimzal spaning parameter for a localized regression model, as well as techniques to estimate confidence intervals using a bootstrap.
http://blogs.mathworks.com/loren/2011/01/13/data-driven-fitting/
I'm doing some work on tracking moving objects using a ceiling mounted downward facing camera. I've got to the point where I can detect the position of the desired object in each frame.
I'm looking into using a Kalman filter to track the object's position and speed through the scene and I've reached a stumbling block. I've set up my system and have all the required parts of the Kalman filter except the measurement variance.
I want to be able to assign a meaningful variance to each measurement to allow the correction phase to use the new information in a sensible manner. I have several measures assigned to my detected objects which could in theory be useful in determining how accurate the position should be and it seems logical to try and combine them to derive a suitable variance.
Am I approaching this in the right manner and if so, can anyone point me in the right direction to continue?
Any help greatly appreciated.
I think you are right. According to this post:
Sensor fusioning with Kalman filter
determining the variance is 100% experimental. It seems to me you have everything you need to get good estimates of the variance.
sorry for the late reply. I have personally encountered the same problem in my previous project. I found the advice given by Gustaf Hendeby in his Sensor Fusion lecture slides ( Page 10 of the slides) extremely valuable.
To summarize:
(1) The SNR of your measurement noise and your process noise determines your filter behavior. A high process noise/measurement noise ration makes your filter slower (low-pass filter), which will usually allow smoother tracking, vice versa a if you set your measurement noise low, you essentially have a high pass filter, which tends to have more jitter.
(2) There are numerous papers in the literature discuss on how to set these noise model properly. However, usually a lot of "tuning" is needed depends on your application. Usually the measurement noise is what we can measure/characterize based on the hardware specification. Therefore a recommendation is to fix "R" (measurement noise covariance) and tune Q (the process model noise covariance).