If a program displays a pixel at X,Y on a display with resolution A, can I precisely predict at what coordinates the same pixel will display at resolution B?
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The 2 display resolutions are:
A-->1366 x 768
B-->1600 x 900
Dividing the max resolutions in each direction yields:
X-direction scaling factor = 1600/1366 = 1.171303075
Y-direction scaling factor = 900/768 = 1.171875
Say for example that the only red pixel on display A occurs at pixel (1,1). If I merely scale up using these factors, then on display B, that red pixel will be displayed at pixel (1.171303075, 1.171875). I'm not sure how to interpret that, as I'm used to thinking of pixels as integer values. It might help if I knew the exact geometry of pixel coordinates/placement on a screen. e.g., do pixel coordinates (1,1) mean that the center of the pixel is at (1,1)? Or a particular corner of the pixel is at (1,1)? I'm sure diagrams would assist in visualizing this--if anyone can post a link to helpful resources, I'd appreciate it. And finally, I may be approaching this all wrong.
Thanks in advance.
I think, your problem is related to the field of scaling/resampling images. Bitmap-, or raster images are digital photographs, so they are the most common form to represent natural images that are rich in detail. The term bitmap refers to how a given pattern (bits in a pixel) maps to a specific color. A bitmap images take the form of an array, where the value of each element, called a pixel picture element, correspond to the color of that region of the image.
Sampling
When measuring the value for a pixel, one takes the average color of an area around the location of the pixel. A simplistic model is sampling a square, and a more accurate measurement is to calculate a weighted Gaussian average. When perceiving a bitmap image the human eye should blend the pixel values together, recreating an illusion of the continuous image it represents.
Raster dimensions
The number of horizontal and vertical samples in the pixel grid is called raster dimensions, it is specified as width x height.
Resolution
Resolution is a measurement of sampling density, resolution of bitmap images give a relationship between pixel dimensions and physical dimensions. The most often used measurement is ppi, pixels per inch.
Scaling / Resampling
Image scaling is the name of the process when we need to create an image with different dimensions from what we have. A different name for scaling is resampling. When resampling algorithms try to reconstruct the original continuous image and create a new sample grid. There are two kind of scaling: up and down.
Scaling image down
The process of reducing the raster dimensions is called decimation, this can be done by averaging the values of source pixels contributing to each output pixel.
Scaling image up
When we increase the image size we actually want to create sample points between the original sample points in the original raster, this is done by interpolation the values in the sample grid, effectively guessing the values of the unknown pixels. This interpolation can be done by nearest-neighbor interpolation, bilinear interpolation, bicubic interpolation, etc. But the scaled up/down image must be also represented over discrete grid.
Related
I am looking for a workflow that would clean (and possibly straighten) old and badly scanned images of musical scores (like the one below).
I've tried to use denoise, hough filters, imagemagick geometry filters, and I am struggling to identify the series of filters that remove the scanner noise/bias.
Just some quick ideas:
Remove grayscale noise: Do a low pass filter (darks), since the music is darker than a lot of the noise. Remaining noise is mostly vertical lines.
Rotate image: Sum grayscale values for each column of the image. You'll get a vector with the total pixel lightness in that column. Use gradient descent or search on the rotation of the image (within some bounds like +/-15deg rotation) to maximize the variance of that vector. Idea here is that the vertical noise lines indicate vertical alignment, and so we want the columns of the image to align with these noise lines (= maximized variance).
Remove vertical line noise: After rotation, take median value of each column. The greater the distance (squared difference) a pixel is from that median darkness, the more confident we are it is its true color (e.g. a pure white or black pixel when vertical noise was gray). Since noise is non-white, you could try blending this distance by the whiteness of the median for an alternative confidence metric. Ideally, I think here you'd train some 7x7x2 convolution filter (2 channels being pixel value and distance from median) to estimate true value of the pixel. That would be the most minimal machine learning approach, not using some full-fledged NN. However, given your lack of training data, we'll have to come up with our own heuristic for what the true pixel value is. You likely will need to play around with it, but here's what I think might work:
Set some threshold of confidence; above that threshold we take the value as is. Below the threshold, set to white (the binary expected pixel value for the entire page).
For all values below threshold, take the max confidence value within a +/-2 pixels L1 distance (e.g. 5x5 convolution) as that pixel's value. Seems like features are separated by at least 2 pixels, but for lower resolutions that window size may need to be adjusted. Since white pixels may end up being more confident overall, you could experiment with prioritizing darker pixels (increase their confidence somehow).
Clamp the image contrast and maybe run another low pass filter.
Light Field captures the scene from slightly different points. This means I would have two images of the same scene with a slight shift, as shown in the following figure:
Assuming the red squares in the images above are pixels. I know that the spatial difference between those two pixels is a shift. Nevertheless, what other information do these two pixels give us in terms of scene radiance? I mean is there a way to find (or compute) the difference in image irradiance values between those two points?
Look for color space representations other than RGB. Some of them have explicit channel(s) carrying luminance information of a pixel.
A varaiant of the same idea is to convert to a Black and White image and examine the pixel values.
I am looking for a "very" simple way to check if an image bitmap is blur. I do not need accurate and complicate algorithm which involves fft, wavelet, etc. Just a very simple idea even if it is not accurate.
I've thought to compute the average euclidian distance between pixel (x,y) and pixel (x+1,y) considering their RGB components and then using a threshold but it works very bad. Any other idea?
Don't calculate the average differences between adjacent pixels.
Even when a photograph is perfectly in focus, it can still contain large areas of uniform colour, like the sky for example. These will push down the average difference and mask the details you're interested in. What you really want to find is the maximum difference value.
Also, to speed things up, I wouldn't bother checking every pixel in the image. You should get reasonable results by checking along a grid of horizontal and vertical lines spaced, say, 10 pixels apart.
Here are the results of some tests with PHP's GD graphics functions using an image from Wikimedia Commons (Bokeh_Ipomea.jpg). The Sharpness values are simply the maximum pixel difference values as a percentage of 255 (I only looked in the green channel; you should probably convert to greyscale first). The numbers underneath show how long it took to process the image.
If you want them, here are the source images I used:
original
slightly blurred
blurred
Update:
There's a problem with this algorithm in that it relies on the image having a fairly high level of contrast as well as sharp focused edges. It can be improved by finding the maximum pixel difference (maxdiff), and finding the overall range of pixel values in a small area centred on this location (range). The sharpness is then calculated as follows:
sharpness = (maxdiff / (offset + range)) * (1.0 + offset / 255) * 100%
where offset is a parameter that reduces the effects of very small edges so that background noise does not affect the results significantly. (I used a value of 15.)
This produces fairly good results. Anything with a sharpness of less than 40% is probably out of focus. Here's are some examples (the locations of the maximum pixel difference and the 9×9 local search areas are also shown for reference):
(source)
(source)
(source)
(source)
The results still aren't perfect, though. Subjects that are inherently blurry will always result in a low sharpness value:
(source)
Bokeh effects can produce sharp edges from point sources of light, even when they are completely out of focus:
(source)
You commented that you want to be able to reject user-submitted photos that are out of focus. Since this technique isn't perfect, I would suggest that you instead notify the user if an image appears blurry instead of rejecting it altogether.
I suppose that, philosophically speaking, all natural images are blurry...How blurry and to which amount, is something that depends upon your application. Broadly speaking, the blurriness or sharpness of images can be measured in various ways. As a first easy attempt I would check for the energy of the image, defined as the normalised summation of the squared pixel values:
1 2
E = --- Σ I, where I the image and N the number of pixels (defined for grayscale)
N
First you may apply a Laplacian of Gaussian (LoG) filter to detect the "energetic" areas of the image and then check the energy. The blurry image should show considerably lower energy.
See an example in MATLAB using a typical grayscale lena image:
This is the original image
This is the blurry image, blurred with gaussian noise
This is the LoG image of the original
And this is the LoG image of the blurry one
If you just compute the energy of the two LoG images you get:
E = 1265 E = 88
or bl
which is a huge amount of difference...
Then you just have to select a threshold to judge which amount of energy is good for your application...
calculate the average L1-distance of adjacent pixels:
N1=1/(2*N_pixel) * sum( abs(p(x,y)-p(x-1,y)) + abs(p(x,y)-p(x,y-1)) )
then the average L2 distance:
N2= 1/(2*N_pixel) * sum( (p(x,y)-p(x-1,y))^2 + (p(x,y)-p(x,y-1))^2 )
then the ratio N2 / (N1*N1) is a measure of blurriness. This is for grayscale images, for color you do this for each channel separately.
Assuming that I have a grayscale (8-bit) image and assume that I have an integral image created from that same image.
Image resolution is 720x576. According to SURF algorithm, each octave is composed of 4 box filters, which are defined by the number of pixels on their side. The
first octave uses filters with 9x9, 15x15, 21x21 and 27x27 pixels. The
second octave uses filters with 15x15, 27x27, 39x39 and 51x51 pixels.The third octave uses filters with 27x27, 51x51, 75x75 and 99x99 pixels. If the image is sufficiently large and I guess 720x576 is big enough (right??!!), a fourth octave is added, 51x51, 99x99, 147x147 and 195x195. These
octaves partially overlap one another to improve the quality of the interpolated results.
// so, we have:
//
// 9x9 15x15 21x21 27x27
// 15x15 27x27 39x39 51x51
// 27x27 51x51 75x75 99x99
// 51x51 99x99 147x147 195x195
The questions are:What are the values in each of these filters? Should I hardcode these values, or should I calculate them? How exactly (numerically) to apply filters to the integral image?
Also, for calculating the Hessian determinant I found two approximations:
det(HessianApprox) = DxxDyy − (0.9Dxy)^2 anddet(HessianApprox) = DxxDyy − (0.81Dxy)^2Which one is correct?
(Dxx, Dyy, and Dxy are Gaussian second order derivatives).
I had to go back to the original paper to find the precise answers to your questions.
Some background first
SURF leverages a common Image Analysis approach for regions-of-interest detection that is called blob detection.
The typical approach for blob detection is a difference of Gaussians.
There are several reasons for this, the first one being to mimic what happens in the visual cortex of the human brains.
The drawback to difference of Gaussians (DoG) is the computation time that is too expensive to be applied to large image areas.
In order to bypass this issue, SURF takes a simple approach. A DoG is simply the computation of two Gaussian averages (or equivalently, apply a Gaussian blur) followed by taking their difference.
A quick-and-dirty approximation (not so dirty for small regions) is to approximate the Gaussian blur by a box blur.
A box blur is the average value of all the images values in a given rectangle. It can be computed efficiently via integral images.
Using integral images
Inside an integral image, each pixel value is the sum of all the pixels that were above it and on its left in the original image.
The top-left pixel value in the integral image is thus 0, and the bottom-rightmost pixel of the integral image has thus the sum of all the original pixels for value.
Then, you just need to remark that the box blur is equal to the sum of all the pixels inside a given rectangle (not originating in the top-lefmost pixel of the image) and apply the following simple geometric reasoning.
If you have a rectangle with corners ABCD (top left, top right, bottom left, bottom right), then the value of the box filter is given by:
boxFilter(ABCD) = A + D - B - C,
where A, B, C, D is a shortcut for IntegralImagePixelAt(A) (B, C, D respectively).
Integral images in SURF
SURF is not using box blurs of sizes 9x9, etc. directly.
What it uses instead is several orders of Gaussian derivatives, or Haar-like features.
Let's take an example. Suppose you are to compute the 9x9 filters output. This corresponds to a given sigma, hence a fixed scale/octave.
The sigma being fixed, you center your 9x9 window on the pixel of interest. Then, you compute the output of the 2nd order Gaussian derivative in each direction (horizontal, vertical, diagonal). The Fig. 1 in the paper gives you an illustration of the vertical and diagonal filters.
The Hessian determinant
There is a factor to take into account the scale differences. Let's believe the paper that the determinant is equal to:
Det = DxxDyy - (0.9 * Dxy)^2.
Finally, the determinant is given by: Det = DxxDyy - 0.81*Dxy^2.
Look at page 17 of this document
http://www.sci.utah.edu/~fletcher/CS7960/slides/Scott.pdf
If you made a code for normal Gaussian 2D convolution, just use the box filter as a Gaussian kernel and the input image will be the same original image not integral image. The results from this method will be same with the one you asked.
When we look at a photo of a group of trees, we are able to identify that the photo is predominantly green and brown, or for a picture of the sea we are able to identify that it is mostly blue.
Does anyone know of an algorithm that can be used to detect the prominent color or colours in a photo?
I can envisage a 3D clustering algorithm in RGB space or something similar. I was wondering if someone knows of an existing technique.
Convert the image from RGB to a color space with brightness and saturation separated (HSL/HSV)
http://en.wikipedia.org/wiki/HSL_and_HSV
Then find the dominating values for the hue component of each pixel. Make a histogram for the hue values of each pixel and analyze in which angle region the peaks fall in. A large peak in the quadrant between 180 and 270 degrees means there is a large portion of blue in the image, for example.
There can be several difficulties in determining one dominant color. Pathological example: an image whose left half is blue and right half is red. Also, the hue will not deal very well with grayscales obviously. So a chessboard image with 50% white and 50% black will suffer from two problems: the hue is arbitrary for a black/white image, and there are two colors that are exactly 50% of the image.
It sounds like you want to start by computing an image histogram or color histogram of the image. The predominant color(s) will be related to the peak(s) in the histogram.
You might want to change the image from RGB to indexed, then you could use a regular histogram and detect the pics (Matlab does this with rgb2ind(), as you probably already know), and then the problem would be reduced to your regular "finding peaks in an array".
Then
n = hist(Y,nbins) bins the elements in vector Y into 10 equally spaced containers and returns the number of elements in each container as a row vector.
Those values in n will give you how many elements in each bin. Then it's just a matter of fiddling with the number of bins to make them wide enough, and with how many elements in each would make you count said bin as a predominant color, then taking the bins that contain those many elements, calculating the index that corresponds with their middle, and converting it to RGB again.
Whatever you're using for your processing probably has similar functions to those
Average all pixels in the image.
Remove all pixels that are farther away from the average color than standard deviation.
GOTO 1 with remaining pixels until arbitrarily few are left (1 or maybe 1%).
You might also want to pre-process the image, for example apply high-pass filter (removing only very low frequencies) to even out lighting in the photo — http://en.wikipedia.org/wiki/Checker_shadow_illusion