I'm looking for algorithms that can combine images based on a quality factor. For example, you have 50-100 photographies of the same scene, but some areas had bad quality in some image because artefacts or whatever.
Now for each pixel I select the best one with a quality factor based in darkness but for sure we have a lot off possible combinations and a lot a quality measures pixel/patch/image-based.
I'm trying to research about this topic but I don't found how to describe it properly, do you know some algorithms or at least which is de name of this "problem"?
Update: Note some desired pixels or pixel areas only appears in a few cases, e.g. in 10 of 100 images. It causes we can't use simple averaging or similar methods.
One of the solution is averaging the images.
If you have quality factor for each sample than u can do weighted averaging.
You use following alogorithm to improve over averaging : -
Divide image into block of 4*4 or 8*8
calculate autocorrelation in all such blocks
Higher autocorrelation means lesser noise hence u can give quality factor high for autocorrealation and low otherwise.
Do weighted averaging averaging of blocks using the quality factor defined
Related
I'm working on a side project that will accept a source image and then produce a photo mosaic using a set of thumbnailed images it has available. I have an implementation that works OK (see below) but I'm running up against "big O" issues trying to increase the number of available images for replacement.
The process I'm currently using is the following:
I pre-calculated 4 bucket RGB color histograms for all the available replacement images
Scale up the source image to 1000x1000
Create 20x20 "tiles" from the scaled source image and create 4 bucket RGB histograms for each tile
For each tile, calculate the Chi-squared distance for each of the available replacement images
For each tile, select the replacement image with the smallest Chi-squared distance
So concretely, the problem I'm running into as the number of available replacement images increases the number of comparisons grows exponentially. I'm currently testing with 25,000 available replacement images and it takes nearly 10 minutes to generate the final image across 4 cores on my laptop.
My question is, is there an approach I can use to avoid having the number of distance calculations grow exponentially?
One idea I had was calculating the distances between each of the goal "tiles", separating them into some N groups, finding an average histogram within the group and then finding the closest K available images to the average histogram. From there, I'd go back and calculate the closest matches for the tiles within each group but from a smaller source of the K closest images.
The pragmatic answer is cheat.
Define several aggregate projections, like "average R", "average G", "average B". Precategorize your images on these projections. Do a preliminary score for each section to the thumbnails which is the sum of absolute differences between the image's projection and the thumbnails.
Now throw the thumbnails into a heap, and pull off the best 50. Do your detailed calculation on that 50 and select the best one of those.
You might not pick the perfect answer. But you'll pick a pretty good one. And your necessary work per thumbnail is very small. 400 times you do 3 lookups, and a couple of comparisons. Only a few make the cut to the real work.
Why are the basis blocks corresponding to reflected waves in the quantisation matrix given seemingly random priorities in the standard JPEG quantisation matrices. Also, why aren't the priorities monotonic with respect to frequency?
I haven't been able to find any explanation and all I can come up with is possible tiling patterns occurring with symmetric quantisation matrices or an adaptation to the arrangement of photoreceptors in the eye.
The quantization tables are a set of fudge factors that attempt to model human perception.
The specific quantization table values are more art than science, because human perception is quirky and complex, and ideal coefficients depend on specific viewing conditions that can only be roughly guessed in advance.
Tables are not always monotonic with respect to frequency, because blocks of certain frequencies form patterns that are more useful than others, e.g. for straight horizontal and vertical lines.
I am new in image processing and I don't know the use of basic terms, I know the basic definition of sparsity, but can anyone please elaborate the definition in term of image processing?
Well Sajid, I actually was doing image processing a few months ago, and I had found a website that gave me what I thought was the best definition of sparsity.
Sparsity and density are terms used to describe the percentage of
cells in a database table that are not populated and populated,
respectively. The sum of the sparsity and density should equal 100%.
A table that is 10% dense has 10% of its cells populated with non-zero
values. It is therefore 90% sparse – meaning that 90% of its cells are
either not filled with data or are zeros.
I took this in the context of on/off for black and white image processing. If many pixels were off, then the pixels were sparse.
As The Obscure Question said, sparsity is when a vector or matrix is mostly zeros. To see a real world example of this, just look at the wavelet transform, which is known to be sparse for any real-world image.
(all the black values are 0)
Sparsity has powerful impacts. It can transform matrix multiplication of two NxN matrices, normally a O(N^3) operation, into an O(k) operation (with k non-zero elements). Why? Because it's a well-known fact that for all x, x * 0 = 0.
What does sparsity mean? In the problems I've been exposed to, it means similarity in some domain. For example, natural images are largely the same color in areas (the sky is blue, the grass is green, etc). If you take the wavelet transform of that natural image, the output is sparse through the recursive nature of the wavelet (well, at least recursive in the Haar wavelet).
I have implemented a nice algorithm ("Non Local Means") for reducing noise in image.
It is based on it's Matlab implementation.
The problem with NLMeans is that the original algorithm is slow even on compiled languages like c/c++ and i am trying to run it using scripting language.
One of best solutions is to use improved Blockwise NLMeans algorithm which is ~60-80 times faster. The problem is that the paper which describes it is written in a complex mathematical language and it's really hard for me to understand an idea and program it
(yes, i didn't learn math at college).
That is why i am desperately looking for a pseudo code of this algorithm.
(modification of original Matlab implementation would be just perfect)
I admit, I was intrigued until I saw the result – 260+ seconds on a dual core, and that doesn't assume the overhead of a scripting language, and that's for the Optimized Block Non Local Means filter.
Let me break down the math for you – My idea of pseudo-code is writing in Ruby.
Non Local Means Filtering
Assume an image that's 200 x 100 pixels (20000 pixels total), which is a pretty tiny image. We're going to have to go through 20,000 pixels and evaluate each one on the weighted average of the other 19,999 pixels: [Sorry about the spacing, but the equation is interpreted as a link without it]
NL [v] (i) = ∑ w(i,j)v(j) [j ∈ I]
where 0 ≤ w(i,j) ≤ 1 and ∑j w(i,j) = 1
Understandably, this last part can be a little confusing, but this is really nothing more than a convolution filter the size of the whole image being applied to each pixel.
Blockwise Non Local Means Filtering
The blockwise implementation takes overlapping sets of voxels (volumetric pixels - the implementation you pointed us to is for 3D space). Presumably, taking a similar approach, you could apply this to 2D space, taking sets of overlapping pixels. Let's see if we can describe this...
NL [v] (ijk) = 1/|Ai|∑ w(ijk, i)v(i)
Where A is a vector of the pixels to be estimated, and similar circumstances as above are applied.
[NB: I may be slightly off; It's been a few years since I did heavy image processing]
Algorithm
In all likelihood, we're talking about reducing complexity of the algorithm at a minimal cost to reduction quality. The larger the sample vector, the higher the quality as well as the higher the complexity. By overlapping then averaging the sample vectors from the image then applying that weighted average to each pixel we're looping through the image far fewer times.
Loop through the image to collect the sample vectors and store their weighted average to an array.
Apply each weighted average (a number between 0 and 1) to each pixel times the pixels value.
Pretty simple, but the processing time is going to be horrid with larger images.
Final Thoughts
You're going to have to make some tough decisions. If you're going to use a scripting language, you're already dealing with significant interpretive overhead. It's far from optimal to use a scripting language for heavy duty image processing. If you're not processing medical images, in all likelihood, there are far better algorithms to use with lesser O's.
Hope this is helpful... I'm not terribly good at making a point clearly and concisely, so if I can clarify anything, let me know.
I'm reading data from a device which measures distance. My sample rate is high so that I can measure large changes in distance (i.e. velocity) but this means that, when the velocity is low, the device delivers a number of measurements which are identical (due to the granularity of the device). This results in a 'stepped' curve.
What I need to do is to smooth the curve in order to calculate the velocity. Following that I then need to calculate the acceleration.
How to best go about this?
(Sample rate up to 1000Hz, calculation rate of 10Hz would be ok. Using C# in VS2005)
The wikipedia entry from moogs is a good starting point for smoothing the data. But it does not help you in making a decision.
It all depends on your data, and the needed processing speed.
Moving Average
Will flatten the top values. If you are interrested in the minimum and maximum value, don't use this. Also I think using the moving average will influence your measurement of the acceleration, since it will flatten your data (a bit), thereby acceleration will appear to be smaller. It all comes down to the needed accuracy.
Savitzky–Golay
Fast algorithm. As fast as the moving average. That will preserve the heights of peaks. Somewhat harder to implement. And you need the correct coefficients. I would pick this one.
Kalman filters
If you know the distribution, this can give you good results (it is used in GPS navigation systems). Maybe somewhat harder to implement. I mention this because I have used them in the past. But they are probably not a good choice for a starter in this kind of stuff.
The above will reduce noise on your signal.
Next you have to do is detect the start and end point of the "acceleration". You could do this by creating a Derivative of the original signal. The point(s) where the derivative crosses the Y-axis (zero) are probably the peaks in your signal, and might indicate the start and end of the acceleration.
You can then create a second degree derivative to get the minium and maximum acceleration itself.
You need a smoothing filter, the simplest would be a "moving average": just calculate the average of the last n points.
The question here is, how to determine n, can you tell us more about your application?
(There are other, more complicated filters. They vary on how they preserve the input data. A good list is in Wikipedia)
Edit!: For 10Hz, average the last 100 values.
Moving averages are generally terrible - but work well for white noise. Both moving averages & Savitzky-Golay both boil down to a correlation - and therefore are very fast and could be implemented in real time. If you need higher order information like first and second derivatives - SG is a good right choice. The magic of SG lies in the constant correlation coefficients needed for the filter - once you have decided the length and degree of polynomial to fit locally, the coefficients need only to be found once. You can compute them using R (sgolay) or Matlab.
You can also estimate a noisy signal's first derivative via the Savitzky-Golay best-fit polynomials - these are sometimes called Savitzky-Golay derivatives - and typically give a good estimate of the first derivative.
Kalman filtering can be very effective, but it's heavier computationally - it's hard to beat a short convolution for speed!
Paul
CenterSpace Software
In addition to the above articles, have a look at Catmull-Rom Splines.
You could use a moving average to smooth out the data.
In addition to GvSs excellent answer above you could also consider smoothing / reducing the stepping effect of your averaged results using some general curve fitting such as cubic or quadratic splines.