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Raster Band Calculations in C# using gdal_calc

I have two raster files in JP2 format. I need to combine the two and perform a calculation against the bands. Is there any way to do this in .NET and C#? Most references I see to performing this use Gdal's calc function in python.
I have tried utilizing the Gdal.Core and Gdal.Core.WindowsRuntime, but I don't see any wrappers for the Calculate call. Has anyone attempted to do this before, and, if so, how did you manage to make the call, or what library did you use?
Thanks,

In C# you need to do it manually as far as I know, you have to open both Datasets, get the bands that you need, make the calculations on them, and then Create a new output file, writing each of the new data to a different band.
There are some examples in the GDAL/OGR In CSharp page here:
https://trac.osgeo.org/gdal/browser/trunk/gdal/swig/csharp/apps
For rasters you'll need to read carefully GDALReadDirect.cs and GDALDatasetRasterIO.cs
If you really see that what you want to do has a simpler solution in Python I would do that instead.
GIS Stack Exchange is a good place to ask questions on these topics.

Schedule with Constraints

I want to schedule tasks with Constraints (similar to the job shop scheduling problem) and thought I could use something like the Microsoft Solver Foundation (I need to use C#). But as far as I know you can only solve problems by finding the optimal maximal or minimal which takes way to long. I need an approximation so the scheduling is not optimal (as good as possible) concerning the total time but all the Constraints are fulfilled.
Any ideas how to approach this problem?

I would suggest you using Z3 solver. It provides you C# API. Basically, it is a SMT solver, which searches for 'good enough' solution with respect to given constraints. It could be rather difficult to define your problem in SMTLIB language.
If it's too hard for you, look at Minizinc or Clingo solvers - just generate problem formulation as a text file, run a solver as a separate process from your C# code, parse solution back from output text file.
EDIT
If you want to minimize a length of a schedule, you can try the following approach. Let's assume that there is a schedule of length K. Is your planning problem satisfiable under this assumption? Let's call a solver to find this out! Generate several problems with different K's and run the solver iteratively. Use binary search to reduce the number of trials.

Identify if an image contains any image (object) from a database

Despite Googling around a fair amount, the only things that surfaced were on neural networks and using existing APIs to find tags about an image, and on webcam tracking.
What I would like to do is create my own data set for some objects (a database containing the images of a product (or a fingerprint of each image), and manufacturer information about the product), and then use some combination of machine learning and object detection to find if a given image contains any product from the data I've collected.
For example, I would like to take a picture of a chair and compare that to some data to find which chair is most likely in the picture from the chairs in my database.
What would be an approach to tackling this problem? I have already considered using OpenCV, and feel that this is a starting point and probably how I'll detect the object, but I've not found how to use this to solve my problem.

I think in the end it doesn't matter what tool you use to tackle your problem. You will probably need some kind of machine learning. It's hard to say which method would result in the best detection, for this I'd recommend to use a tool like weka. It's a collection of multiple machine learning algorithms and lets you easily try out what works best for you.
Before you can start trying out the machine learning you will first need to extract some features out of your dataset. Since you can hardly compare the images pixel by pixel which would result in huge computational effort and does not even necessarily provide the needed results. Try to extract features which make your images unique, like average colour or brightness, maybe try to extract some shapes or sizes out of the image. So in the end you will feed your algorithm just with the features you extracted out of your images and not the images itself.
Which are good features is hard to define, it depends on your special case. Generally it helps to have not just one but multiple features covering completely different aspects of the image. To extract the features you could use openCV, or any other image processing tool you like. Get the features of all images in your dataset and get started with the machine learning.

From what I understood, you want to build a Content Based Image Retrieval system.
There are plenty of methods to do this. What defines the best method to solve your problem has to do with:
the type of objects you want to recognize,
the type of images that will be introduced to search the objects,
the priorities of your system (efficiency, robustness, etc.).
You gave the example of recognizing chairs. In your system which would be the determining factor for selecting the most similar chair? The color of the chair? The shape of the chair? These are typical question that you have to answer before choosing the method.
Either way one of the most used methods to solve such problems is the Bag-of-Words model (also Referred the Bag of Features). I wish I could help more but for that I need that you explain it better which are the final goals of your work / project.

calculating fft with complex number in c#

I use this formula to get frequency of a signal but I dont understand how to implement code with complex number? There is "i" in formula that relates Math.Sqrt(-1). How can I code this formula to signal in C# with NAduio library?

If you want to go back to a basic level then:
You'll want to use some form of probabilistic model, something like a hidden Markov model (HMM). This will allow you to test what the user says to a collection of models, one for each word they are allowed to say.
Additionally you want to transform the audio waveform into something that your program can more easily interpret. Something like a fast Fourier transform (FFT) or a wavelet transform (CWT).
The steps would be:
Get audio
Remove background noise
Transform via FFT or CWT
Detect peaks and other features of the audio
Compare these features with your HMMs
Pick the HMM with the best result about a threshold.
Of course this requires you to previously train the HMMs with the correct words.

A lot of languages actually provide Libraries for this that come, built in. One example, in C#.NET, is at this link. This gives you a step by step guide to how to set up a speech recognition program. It also abstracts you away from the low level detail of parsing audio for certain phenomes etc (which frankly is pointless with the amount of libraries there are about, unless you wish to write a highly optimized version).

It is a difficult problem nonetheless and you will have to use a ASR framework to do it. I have done something slightly more complex (~100 words) using Sphinx4. You can also use HTK.
In general what you have to do is:
write down all the words that you want to recognize
determine the syntax of your commands like (direction) (amount)
Then choose a framework, get an acoustic model, generate a dictionary and a language model compatible with that framework. Then integrate the framework into your application.
I hope I have mentioned all important things you need to do. You can google them separately or go to your chosen framework's tutorial.
Your task is relatively simple in terms of speech recognition and you should get good results if you complete it.

ECG digital signal processing in C#

I'm looking for a C# .NET library for digital filtering (lowpass, highpass, notch) to filter ECG waveforms in real-time. Any suggestions?

If this is non commercial use, I have heard good things about the Signal Lab library. It is free for non commercial use, $570 for commercial use. It it a bit overkill if you are just needing low pass, high pass, and band pass filters. but it does come with controls for visualizing the data if you do not have any yet.
If you just need the filters you may just want to write your own code for the 3 filters. You can check the wikipedia pages for psudocode examples of a Low-pass filter and High-pass filter, I did not quickly find a code example of a noch filter.
Here are some C examples of various filters, to help give you a clue on what you need to do.

If your data is arriving in discrete chunks, I would use Reactive Extensions. This allows the input to control what happens next (reacting to data) instead of using "pull" operations. You can then react to this data by passing it through filters, and then react to that data by displaying it or performing additional calculations.
If you only need notch, high, and low filters, these are trivial to write. As each chunk of data arrives, you can decide whether or not to pass it to the next step (or whether or not to modify the data first). I would imagine you could write this whole section of code in less than 20 lines (maybe less than 10) using Rx. It would result in some pretty elegant code for this use case.

As far as I know you can write your own, because I did.
This should be a good starter for you (coded in C++ but you can easily covert the syntax to C#) - http://www.codeproject.com/KB/cpp/ecg_dsp.aspx
Third party libraries wouldn't be very flexible on the filter equation parameters. As you only will know the characteristics of your signal (amplitudes, frequency band and sampling etc.)
I recommend using a waveshaping algorithm first to get a smooth signal on the C# side before you apply filters, if your ECG sampling rate is low.