I am currently working on OCR software and my idea is to use templates to try to recognize data inside invoices.
However scanned invoices can have several 'flaws' with them:
Not all invoices, based on a single template, are correctly aligned under the scanner.
People can write on invoices
etc.
Example of invoice: (Have to google it, sadly cannot add a more concrete version as client data is confidential obviously)
I find my data in the invoices based on the x-values of the text.
However I need to know the scale of the invoice and the offset from left/right, before I can do any real calculations with all data that I have retrieved.
What have I tried so far?
1) Making the image monochrome and use the left and right bounds of the first appearance of a black pixel. This fails due to the fact that people can write on invoices.
2) Divide the invoice up in vertical sections, use the sections that have the highest amount of black pixels. Fails due to the fact that the distribution is not always uniform amongst similar templates.
I could really use your help on (1) how to identify important points in invoices and (2) on what I should focus as the important points.
I hope the question is clear enough as it is quite hard to explain.
Detecting rotation
I would suggest you start by detecting straight lines.
Look (perhaps randomly) for small areas with high contrast, i.e. mostly white but a fair amount of very black pixels as well. Then try to fit a line to these black pixels, e.g. using least squares method. Drop the outliers, and fit another line to the remaining points. Iterate this as required. Evaluate how good that fit is, i.e. how many of the pixels in the observed area are really close to the line, and how far that line extends beyond the observed area. Do this process for a number of regions, and you should get a weighted list of lines.
For each line, you can compute the direction of the line itself and the direction orthogonal to that. One of these numbers can be chosen from an interval [0°, 90°), the other will be 90° plus that value, so storing one is enough. Take all these directions, and find one angle which best matches all of them. You can do that using a sliding window of e.g. 5°: slide accross that (cyclic) region and find a value where the maximal number of lines are within the window, then compute the average or median of the angles within that window. All of this computation can be done taking the weights of the lines into account.
Once you have found the direction of lines, you can rotate your image so that the lines are perfectly aligned to the coordinate axes.
Detecting translation
Assuming the image wasn't scaled at any point, you can then try to use a FFT-based correlation of the image to match it to the template. Convert both images to gray, pad them with zeros till the originals take up at most 1/2 the edge length of the padded image, which preferrably should be a power of two. FFT both images in both directions, multiply them element-wise and iFFT back. The resulting image will encode how much the two images would agree for a given shift relative to one another. Simply find the maximum, and you know how to make them match.
Added text will cause no problems at all. This method will work best for large areas, like the company logo and gray background boxes. Thin lines will provide a poorer match, so in those cases you might have to blur the picture before doing the correlation, to broaden the features. You don't have to use the blurred image for further processing; once you know the offset you can return to the rotated but unblurred version.
Now you know both rotation and translation, and assumed no scaling or shearing, so you know exactly which portion of the template corresponds to which portion of the scan. Proceed.
If rotation is solved already, I'd just sum up all pixel color values horizontally and vertically to a single horizontal / vertical "line". This should provide clear spikes where you have horizontal and vertical lines in the form.
p.s. Generated a corresponding horizontal image with Gimp's scaling capabilities, attached below (it's a bit hard to see because it's only one pixel high and may get scaled down because it's > 700 px wide; the url is http://i.stack.imgur.com/Zy8zO.png ).
Related
I don't know much about image processing so please bear with me if this is not possible to implement.
I have several sets of aerial images of the same area originating from different sources. The pictures have been taken during different seasons, under different lighting conditions etc. Unfortunately some images look patchy and suffer from discolorations or are partially obstructed by clouds or pix-elated, as par example picture1 and picture2
I would like to take as an input several images of the same area and (by some kind of averaging them) produce 1 picture of improved quality. I know some C/C++ so I could use some image processing library.
Can anybody propose any image processing algorithm to achieve it or knows any research done in this field?
I would try with a "color twist" transform, i.e. a 3x3 matrix applied to the RGB components. To implement it, you need to pick color samples in areas that are split by a border, on both sides. You should fing three significantly different reference colors (hence six samples). This will allow you to write the nine linear equations to determine the matrix coefficients.
Then you will correct the altered areas by means of this color twist. As the geometry of these areas is intertwined with the field patches, I don't see a better way than contouring the regions by hand.
In the case of the second picture, the limits of the regions are blurred so that you will need to blur the region mask as well and perform blending.
In any case, don't expect a perfect repair of those problems as the transform might be nonlinear, and completely erasing the edges will be difficult. I also think that colors are so washed out at places that restoring them might create ugly artifacts.
For the sake of illustration, a quick attempt with PhotoShop using manual HLS adjustment (less powerful than color twist).
The first thing I thought of was a kernel matrix of sorts.
Do a first pass of the photo and use an edge detection algorithm to determine the borders between the photos - this should be fairly trivial, however you will need to eliminate any overlap/fading (looks like there's a bit in picture 2), you'll see why in a minute.
Do a second pass right along each border you've detected, and assume that the pixel on either side of the border should be the same color. Determine the difference between the red, green and blue values and average them along the entire length of the line, then divide it by two. The image with the lower red, green or blue value gets this new value added. The one with the higher red, green or blue value gets this value subtracted.
On either side of this line, every pixel should now be the exact same. You can remove one of these rows if you'd like, but if the lines don't run the length of the image this could cause size issues, and the line will likely not be very noticeable.
This could be made far more complicated by generating a filter by passing along this line - I'll leave that to you.
The issue with this could be where there was development/ fall colors etc, this might mess with your algorithm, but there's only one way to find out!
So we need to detect whether an image, created by a scanner, represents an empty page. I'm way out of my depth when it comes to image processing, so I have to run this by the community.
Here's what I have come up with so far:
Empty pages can be glaringly white, gray recycled paper, or yellowed old paper. The current idea is to create a histogram for a page, look for a steep increase of the curve, and get the percentage of pixels are darker than that. If that exceeds a threshold, the page is likely not empty.
Since this would likely classify a page containing a single line of text at the top as empty, we would tile the page and gather statistics about each tile.
We would need to detect scanned staplers and holes from binding (likely only in certain tiles), but this can be put off to some later stage. However, if you have an idea what to look out for besides these two, please mention it in a comment.
This needs to be fast. It's part of a document processing workflow that processes (tens of) thousands of pages per day. If processing a page takes ten seconds longer, than our customers will have to tell their customers that they'll have to wait several days longer for their results. (If this results in more false positives, some customers would rather have someone check a few dozen found "empty" pages, than have their customer wait one more day.)
So here's my questions:
Is it a good idea to take this route or is there something better?
If we do it this way, how would I do this? What's a good (cheap) algorithm for finding a threshold for a page? Could we gain significant speed by assuming a similar threshold for a batch of documents? To which precision could brightness values be rounded, before getting logged? What quirks could we expect?
If you know that a scanned page is going to fill the image entirely, then calculating the standard deviation might be a good way of doing this.
I would suggest blurring page slightly to reduce some noise. Then calculate the SD for the page, in theory, a page the is more or less all one colour will have a low SD and one with lots of text will have a higher SD. Then it's a case of 'training' the system to work out when a page is plain and when it is text. You might find that certain pages are hard for it to tell.
You could have it trained by having it process a vast number of pages, and it goes through them all, and you say if it is plain or not.
EDIT
ok, a white page with black text, if we have just the page and no surrounding stuff, will have a mean colour of grey, probably a fairly light grey. Getting the average is a for loop through all the pixels, adding their values and then dividing by the number of pixels. I'm not good with this o(logN) stuff, but suffice to say, it will not that long. Unless you have HUGE images.
SD is a second for loop, this time we are counting up how different each pixel is from the mean, and then dividing by the mean. This will take a bit longer then the mean, as we have to do something like
diff = thispixel - mean;
if(diff < 0) {
diff = -diff;
}
runningTotal += diff;
For a plain coloured page, each pixel will be close to the mean value, thus our SD will be low. If the SD is below a certain value, we can assume that this means the page is all one colour.
This might have problems if their is very minimal amount of text, as it will not have a large influence on the SD, so maybe like you suggested in the question, break the page into sections. I suggest strips horizontally, as text tends to go this way. If we do one of these strips one at a time, once one strip suggests it has text, we can stop as we don't care if the rest is blank or not.
Blurring the page will help reduce noise, as the odd pixel of noise will be reduced in its impact, thus give you a 'tighter' SD. You could also use it to reduce the resolution of your image.
Say you sauce image is 300 wide by 900 high, you could sample pixels in blocks of nine, 3 *3, and thus end up with an image that is 100 wide by 300 high, so it can actually be used to reduce the amount of calculations you need to do, in this case by a ninth!
The main problem is going to be in working out how high an SD can be with just a plain page. Maybe have it find the SD of a load of blank pages.
By the sounds of it, you are probably going to want to have a middle ground that lets it be unsure and ask for human intervention, possibly letting the human value train the system to get better?
Perform some sort of simple edge detection. If the number of pixels constituting edges is below some threshold, then there's going to be a high probability the page is empty. This could be improved by classifying certain edges that correspond with high certainty (by shape and location) to punched holes and staples as trivial and discounting them from the metric.
When I worked for a document processor (~8 years ago), we handled client projects varying from very "clean" only-US-letter-sized pages to cover-/cardstock of irregular shapes mixed with normal pages. Operators fed pre-sorted files into scanning machines and only had to watch for folded corners and similar mechanical problems. Their output was multiple streams of hundreds of images corresponding to a range of files. A single scanner operator could easily scan 15k pieces of paper in a shift (that's only 0.60 pages/sec, while a scanner at speed could handle 3 pages/sec and still scan both sides). Later operators processed those looking for key pages to mark file start and end. (Image recognition can be used here, sometimes, but people also provide a quality check on the first operators.) We had many variables that could be set per client project.
I'm basing the rough outline below on that experience and how it appears that your goals and workflow are similar.
(Terminology: By client I mean our client, e.g. a specific bank. A project or client project is a set of documents from that client that contains many files, e.g. all mortgages handled by a specific branch in a given year. A file is a logical arrangement that would normally be a physical file folder for one of the client's customers, e.g. all mortgage papers for one address.)
Cut off the top, bottom, sides, and corners. Throw these out of your calculations (even though you'll probably store them in the final image). This will cover staple holes, binder holes, but also (tiny) folded corners and very minute torn edges which appear as black spots. Depending on how you're scanning, the last two may be less of a problem.
Vary the sizes of these cuts for each client project, as required. For example, even a very thin edge slice, say 1-2mm, will eliminate most ragged edges without increasing false positive rate.
Convert to black and white, 1 bit per pixel. I suspect you are already doing this for some client projects anyway, so doing this efficiently and effectively, which can be subtle, should be no extra work. (Even if you don't store the 1bpp image as the deliverable result, the conversion will be helpful in empty page detection.) Eliminate noise by dropping any black pixels with none or only one black neighbor (using all surrounding 8 as neighbors).
After cutting extremities (#1) and this simplistic noise reduction, blank pages will have a very low number of black pixels; most blanks will have no black pixels at all – exempting exceptionally poor page quality, inked stamps (when scanning back-sides, mentioned more below), or other circumstances across the whole project, and so forth.
Depending on client project, you may set hotspots to be watched – the converse of cutting off the sides. For example, watching a 1" strip where a single line at the top of the page would appear may reduce false positives. A low contrast scan or faded hardcopy (perhaps even pencil, which can be common on back-sides) with only one line of text will be distinguished from a blank page this way.
What sections are worth watching depends on each project, but do not try to divide the page up into tiles and then subdivide those tiles into areas of interest. Instead, parallelize this on the page level; e.g. 1 worker per core, each worker handles a full page at a time.
Depending on how you're keying individual files, you may find it helpful to drop blanks (before marking start-of-file pages, which is still often a manual process even at high volume) then watch for blank pages at unexpected points after files have been keyed (e.g. expected would be the last page of the file, without being two blanks in a row, etc.).
For example, if a particular project is only scanning one side of each page, then detecting two blank pages in a row is a good indication that a couple pages in a file were flipped upside-down (clients often hand over hardcopy files like this). Either the sorters (who remove things like staples and paperclips) or the first machine operators should have caught this mistake, but, regardless, it will now need a manual check to verify.
On the other hand, there were projects that had very clean files so sorters could insert (usually colored) blank pages marking file boundaries. In this case, the second set of people still did the keying by file number, but only had to examine the first page of each file. This wasn't rare, but not common either.
Before I start rambling a bit, I hope my main point comes across: you have to decide how to mitigate rates of false positives (= data loss) and false negatives (= annoying blanks and otherwise harmless, but a maximum allowed rate may still be specified in the project contract). That varies drastically by project and the type of files/documents you're handling, but it guides you in how to do the detection. You will get much better results from a tailored approach than trying one-size-fits-all, even if the tailored approaches are 80-98% similar.
If you're delivering 1bpp images to the client, for example, you might not even want/need to eliminate blanks as filesize (and ultimately size of the delivered dataset) won't be an issue. This can be an acceptable trade-off when eliminating most blanks is harder while maintaining a low false positive rate; such as for files with inked stamps ("received on", "accepted", "due date", etc.; they bleed through to the back) or other problems, for example.
My fall class does a bunch of image-processing projects.
Here's what I would try:
Project from color to grayscale
Pour all the pixels into a simple histogram with say 100 buckets between 0 and 1
Find a local minimum in the histogram such that the absoluete value of above - below is as small as possible, where above is the number of brighter pixels and below is the number of darker pixels
Force the above pixels to white and the below pixels to black
If you like, as an extra step you could remove black edges
If there are hardly any black pixels, the page is blank
The first two steps should be combined, and they are the only time-consuming steps; on a 600dpi images you may have to touch many millions of pixels. The rest will be lightning fast. I'd be very surprised if you can't classify multiple images per second—especially if you know there will be no black edges.
The only part that requires training or experiment is the last step. It's also possible that you will need to fiddle around with the number of buckets in the histogram; if there are too many buckets, you may have a bad local minimum.
Good luck, and report back to us how you make out!
Check out this line detection algorithm: http://homepages.inf.ed.ac.uk/rbf/HIPR2/linedet.htm. In addition to a detailed explanation of how the algo works there's a demo where you can use your own image and see the results. I tried two images: 1) a B&W scan of a receipt, 2) the B&W, "blank" back side of that same receipt. All of the edge detection algorithms I tried found edges on the "blank" page. But, this line detection algorithm was the only algorithm that correctly found lines on the front page and yet didn't find anything on the "blank" back page.
It looks as if you're trying to convert all paperwork for a company into digital documents. Some of this paper can be really old.
Say your text is black, and any other color is the background. If you take two weighted averages, one consisting of what you think is the text, and one consisting of the background, you can compare those two and see if they're distant enough to consider further evaluation. This will removing any uneven aging of the paper.
Staple holes and punched holes in paper are pretty standard in size, but they'd show up as gray or not at all if you're scanning on a white background. If not, then you can guess where these are and remove them.
Now, we look at areas of high interest, areas where the black pixels are the most dense. Select a portion of that and OCR it. Place the starting top-left closest to an area where text begins. On a typical document, a solid blank linear area going left-to-right and another going top-to-bottom denotes the top and left sides of a paragraph. You can be sure that you got a line of text because below a line of text is another blank left-to-right area. So you don't need to worry about selecting a portion that will chop text in half.
You could take the mean gray level (integer) of each few rows of the scanned image (depending on the resolution and how many lines are required to capture one line of text), then consider the spread of row means. If there is no text on the page, the spread of means should be small (i.e. background ranges from 250-255), and if there is text on the whole page or on part of the page, the spread would be much larger (i.e. 15 for text to 250 for background).
Seems to me like the solution should be computationally simple due to the large number of pages to check. Approaches requiring further processing (edge detection, filtering, etc) seem like overkill, and will take much longer to run.
There is no need to process pixel by pixel, using matrices will help this be more efficient, for example using Numpy you can calculate means, sums, etc. for entire rows, columns or matrices at once much more efficiently. There is also no need to process EVERY pixel, a good sample of rows should be able to accomplish the task with similar accuracy. 8bit accuracy should be fine, and you could even resample to large pixels before running this processing algorithm.
You can do a noisy trim, i.e. blur the image and do an auto-trim (without actually modifying the image). If the width or height of the trim result is below a threshold (e.g. 80 to 100 for a 600 dpi image) then the page is empty.
A proof of concept using the ImageMagick command line front-end:
$ convert scan.png -shave 300x0 -virtual-pixel White -blur 0x15 -fuzz 15% \
-trim info:
The above command assumes a 600 dpi DIN A4 black and white (1 Bit) image. It also ignores a margin of 300 pixels such that artifacts like perforation holes don't yield false negatives.
To give you some background as to what I'm doing: I'm trying to quantitatively record variations in flow of a compressible fluid via image analysis. One way to do this is to exploit the fact that the index of refraction of the fluid is directly related to its density. If you set up some kind of image behind the flow, the distortion in the image due to refractive index changes throughout the fluid field leads you to a density gradient, which helps to characterize the flow pattern.
I have a set of routines that do this successfully with a regular 2D pattern of dots. The dot pattern is slightly distorted, and by comparing the position of the dots in the distorted image with that in the non-distorted image, I get a displacement field, which is exactly what I need. The problem with this method is resolution. The resolution is limited to the number of dots in the field, and I'm exploring methods that give me more data.
One idea I've had is to use a regular grid of horizontal and vertical lines. This image will distort the same way, but instead of getting only the displacement of a dot, I'll have the continuous distortion of a grid. It seems like there must be some standard algorithm or procedure to compare one geometric grid to another and infer some kind of displacement field. Nonetheless, I haven't found anything like this in my research.
Does anyone have some ideas that might point me in the right direction? FYI, I am not a computer scientist -- I'm an engineer. I say that only because there may be some obvious approach I'm neglecting due to coming from a different field. But I can program. I'm using MATLAB, but I can read Python, C/C++, etc.
Here are examples of the type of images I'm working with:
Regular: Distorted:
--------
I think you are looking for the Digital Image Correlation algorithm.
Here you can see a demo.
Here is a Matlab Implementation.
From Wikipedia:
Digital Image Correlation and Tracking (DIC/DDIT) is an optical method that employs tracking & image registration techniques for accurate 2D and 3D measurements of changes in images. This is often used to measure deformation (engineering), displacement, and strain, but it is widely applied in many areas of science and engineering.
Edit
Here I applied the DIC algorithm to your distorted image using Mathematica, showing the relative displacements.
Edit
You may also easily identify the maximum displacement zone:
Edit
After some work (quite a bit, frankly) you can come up to something like this, representing the "displacement field", showing clearly that you are dealing with a vortex:
(Darker and bigger arrows means more displacement (velocity))
Post me a comment if you are interested in the Mathematica code for this one. I think my code is not going to help anybody else, so I omit posting it.
I would also suggest a line tracking algorithm would work well.
Simply start at the first pixel line of the image and start following each of the vertical lines downwards (You just need to start this at the first line to get the starting points. This can be done by a simple pattern that moves orthogonally to the gradient of that line, ergo follows a line. When you reach a crossing of a horizontal line you can measure that point (in x,y coordinates) and compare it to the corresponding crossing point in your distorted image.
Since your grid is regular you know that the n'th measured crossing point on the m'th vertical black line are corresponding in both images. Then you simply compare both points by computing their distance. Do this for each line on your grid and you will get, by how far each crossing point of the grid is distorted.
This following a line algorithm is also used in basic Edge linking algorithms or the Canny Edge detector.
(All this are just theoretic ideas and I cannot provide you with an algorithm to it. But I guess it should work easily on distorted images like you have there... but maybe it is helpful for you)
i'm working in a project to recognize a bit code from an image like this, where black rectangle represents 0 bit, and white (white space, not visible) 1 bit.
Somebody have any idea to process the image in order to extract this informations? My project is written in java, but any solution is accepted.
thanks all for support.
I'm not an expert in image processing, I try to apply Edge Detection using Canny Edge Detector Implementation, free java implementation find here. I used this complete image [http://img257.imageshack.us/img257/5323/colorimg.png], reduce it (scale factor = 0.4) to have fast processing and this is the result [http://img222.imageshack.us/img222/8255/colorimgout.png]. Now, how i can decode white rectangle with 0 bit value, and no rectangle with 1?
The image have 10 line X 16 columns. I don't use python, but i can try to convert it to Java.
Many thanks to support.
This is recognising good old OMR (optical mark recognition).
The solution varies depending on the quality and consistency of the data you get, so noise is important.
Using an image processing library will clearly help.
Simple case: No skew in the image and no stretch or shrinkage
Create a horizontal and vertical profile of the image. i.e. sum up values in all columns and all rows and store in arrays. for an image of MxN (width x height) you will have M cells in horizontal profile and N cells in vertical profile.
Use a thresholding to find out which cells are white (empty) and which are black. This assumes you will get at least a couple of entries in each row or column. So black cells will define a location of interest (where you will expect the marks).
Based on this, you can define in lozenges in the form and you get coordinates of lozenges (rectangles where you have marks) and then you just add up pixel values in each lozenge and based on the number, you can define if it has mark or not.
Case 2: Skew (slant in the image)
Use fourier (FFT) to find the slant value and then transform it.
Case 3: Stretch or shrink
Pretty much the same as 1 but noise is higher and reliability less.
Aliostad has made some good comments.
This is OMR and you will find it much easier to get good consistent results with a good image processing library. www.leptonica.com is a free open source 'C' library that would be a very good place to start. It could process the skew and thresholding tasks for you. Thresholding to B/W would be a good start.
Another option would be IEvolution - http://www.hi-components.com/nievolution.asp for .NET.
To be successful you will need some type of reference / registration marks to allow for skew and stretch especially if you are using document scanning or capturing from a camera image.
I am not familiar with Java, but in Python, you can use the imaging library to open the image. Then load the height and the widths, and segment the image into a grid accordingly, by Height/Rows and Width/Cols. Then, just look for black pixels in those regions, or whatever color PIL registers that black to be. This obviously relies on the grid like nature of the data.
Edit:
Doing Edge Detection may also be Fruitful. First apply an edge detection method like something from wikipedia. I have used the one found at archive.alwaysmovefast.com/basic-edge-detection-in-python.html. Then convert any grayscale value less than 180 (if you want the boxes darker just increase this value) into black and otherwise make it completely white. Then create bounding boxes, lines where the pixels are all white. If data isn't terribly skewed, then this should work pretty well, otherwise you may need to do more work. See here for the results: http://imm.io/2BLd
Edit2:
Denis, how large is your dataset and how large are the images? If you have thousands of these images, then it is not feasible to manually remove the borders (the red background and yellow bars). I think this is important to know before proceeding. Also, I think the prewitt edge detection may prove more useful in this case, since there appears to be less noise:
The previous method of segmenting may be applied, if you do preprocess to bin in the following manner, in which case you need only count the number of black or white pixels and threshold after some training samples.
I'm working on a game, and I've come up with a rather interesting problem: clever ways to draw starfields.
It's a 2D game, so the action can scroll in the X and Y directions. In addition, we can adjust the scale to show more or less of the play area. I'd also like the starfield to have fake parallax to give an impression of depth.
Right now I'm doing this in the traditional way, by having a big array of stars, each of which is tagged by a 'depth' factor. To draw, I translate each star according to the camera position multiplied by the 'depth', so some stars move a lot, and some move a little. This all works fine, but of course since I have a finite number of stars in my array I have issues when the camera moves too far or we zoom out too much. This is will all work, but is involving lots of code and special cases.
This offends my sense of elegance. There has got be a better way of achieving this.
I've considered procedurally generating my stars, which allows me to have an unlimited number: e.g. by using a fixed seed and PRNG to determine the coordinates. I would need to divide the sky up into tiles, generate the seed by hashing the tile coordinates, and then draw, say, 100 stars per tile. This allows me to extend my starfield indefinitely in all directions while still only needing to consider the tiles that are visible --- but this doesn't work with the 'depth' factor, as this allows stars to stray outside their tile. I could simply use multiple layered non-parallax starfields using this algorithm but this strikes me as cheating.
And, of course, I need to do all this every frame, so it's got to be fast.
What do you all reckon?
Have a few layers of stars.
For each layer, use a seeded random number generator (or just an array) to generate the amount of blank space between a star and the next one (a poisson distibution, if you want to be picky about it). You want the stars pretty sparse, so the blank space will often be more than whole row. The back layers will be more dense than the front ones, obviously.
Use this to give yourself several tiles each (say) two screens wide. Scroll the starfield by keeping track of where that "first" star is for each layer.
The player won't notice the tiling, because you scroll the tiles at different rates for each layer, especially if you use a few layers that are each fairly sparse.
As stars in the background don't move as fast as those in the foreground, you could maybe make multi-layer tiles for the background and replace them with one-layer-ones when you've got time to do that. Oh, and how about repeating patterns in the background layers? This would maybe allow you to pregenerate all background tiles - you could still shift them in height and overlay multiple ones with random offsets or so to make it look random.
Is there anything wrong with wrapping the star field around in X and Y? Because of your depth, the wraparound distance should depend on the depth, but you can do that. Each recorded star at (x,y,depth) should appear at all points
[x + j * S * depth, y + k * S * depth]
for all integers j and k. S is a wraparound parameter. If S is 1 then wraparound happens immediately and all stars are always shown somewhere. If S is higher wraparound doesn't happen immediately and some stars are shown off screen. You'll probably want S big enough to ensure no repeats at maximum zoom out.
Each frame, render the stars on one single bitmap/layer. They are only dots, and so it will be faster than using any algorithm with multiple layers.
Now you need an infinite 2D-grid of 3D-boxes filled with a finite number of stars. For each box, you can define an individual RANDOM_SEED value, using its grid-coordinates. The stars in each box can be generated on-the-fly.
Remember to correct the perspective when you zoom: Each 3D-box has a near-rectangle (front-face) and a far-rectangle. You will see more stars of neighbouring boxes, whenever the far-rectangle or near-rectangle shrinks in your view.
Your far-rectangles should never be smaller than half the width of the near-rectangles, otherwise it might be troublesome: You might have to scan huge lists of stars where most of them are out of bounds. You can realize stars behind the far-rectangles via additional 2D-grids of 3D-boxes with other sizes and depths.
Why not combine the coordinates of the starfield 3D boxes to form the random number seed? Use a global "adjustment" if you want to produce different universes. That way you don't need to track the boxes you can't see because the contents are fixed by their location.