I solved this question Maximize the rectangular area under Histogram today.
This left me thinking, are there any real life application to this algorithm ?
If you wanted to attach a label or some text to a histogram inside the bars, one good place to put it is the center of the maximum rectangle.
And even if this particular problem isn't very interesting at first glance, there are a ton of data visualization problems that are related. And the techniques used to solve this problem can be applied elsewhere.
Related
I'm writing an application which measures boxes from pictures. A sample picture after manipulation is shown below:
My application has identified pixels that are part of the box and changed the color to red. You can see that the image is pretty noisy and therefore creates pretty rough looking edges on the rectangle.
I've been reading about edge/corner detection algorithms, but before I pursue one of them I wanted to step back and see if such a complicated algorithm is really necessary. It seems like there probably is a simpler way to go about this, considering I have a few conditions that simplify things:
The image only contains a rectangle, not any other shape.
Each image only has 1 rectangle.
I do not need to be exact, though I'd like to achieve as best fit as I can.
My first go at a simple algorithm involved finding the top most, bottom most, left most and right most points. Those are the 4 corners. That works OK, but isn't super accurate for noisy edges like this. It is easy to eye ball a much better point as the corner.
Can anyone point me towards an algorithm for this?
You have already identified the region of the image that you are interested in(red region).
Using this same logic you should be able to binarize the image. Say the red region then results in white pixels and the rest is black.
Then trace the external contour of the white region using a contour tracing algorithm.
Now you have a point set that represents the external contour of the region.
Find the minimum-area-rectangle that bounds this point set.
You can easily do this using the OpenCV library. Take a look at threshold, findContours, and minAreaRect if you are planning to use OpenCV. Hope this information helps.
I am trying to find a good A* heuristic function for the problem "alien tiles", found at www.alientiles.com for a uni project.
In alien tiles you have a board with NxN tiles, all colored red. By clicking on a tile, all tiles in the same row and column advance by a color, the color order being red->green->blue->purple, resetting to red after purple. The goal is to change all tiles to the specified colors. The simplest goal state is all the tiles going from red to green, blue or purple. The board doesn't have to be 7x7 as the site suggests.
I've thought of summing the difference between each tile and the target tile and dividing by 2N-1 for an NxM board or or finding possible patterns of clicks as the minimum number of clicks, but neither has been working well. I can't think of a way to apply relaxation to the problem or divide it into sub-problems either, since a single click affects an entire row and column.
Of course I'm not asking for anyone to find a solution for me, but some tips or some relevant, simpler problems that I can look at (rubik's cube is such an example that I'm looking at).
Thanks in advance.
The problem you are trying to solve is similar to NIM FOCUS name. Please have a look at it. The solutions for it can be found in Stuart J. Russell book under heuristics section. Hope this helps
Although it is a relatively 'dumb' way of thinking around the problem, one heuristic mechanism i have found that drastically cuts down on the number of states that a star expands, tries to figure out a relationship between the cell that has been clicked most recently and the number of states that clicking on it again would expand. Its like telling a star: "If you have clicked on a cell in your last move, try clicking on another one this time." Obviously in special scenarios,
(e.g. having all the board on your target colour, say green, and only a purple cross where clicking on the center of the cross twice changes the cross colour to green and then you are done)
this way of thinking is actually detrimental. But, it is a place to start.
Please let me know if u figure anything out, as it is something i am working on as well.
I have a "complex" problem where I have a bunch of tooltips (orange) on top of elements (black) that can be randomly placed on screen. The tooltips are a big square with a triangle in the middle of one of it's 4 sides pointing though the element direction. By default, the triangle will be in the middle of the element, but can be moved as long as it stay close to it, so we can't easily understand it refer to this element and not another one.
The problem is, the tooltip must NOT overlap each other, and can't be out of screen.
Image of my tooltip problem
I thought about first placing every tooltips to their default position (triangle pointing down), and then check if they are out of screen or overlap another one, and if so, try another position. But using this technique (which is probably the simplest one), I do not guarantee the best placement since once a tooltip has been placed, I will not replace him if another one can't fit anywhere otherwise it become too complex.
Does someone have any tips/idea how to deal with this type of problem?
Thanks!!
This looks like an instance of the map labelling problem. Wikipedia has an article about it.
You could place all the tooltips using some sort of physical simulation of repulsive electrical charges, similar to what is done in some algorithms for drawing graphs. You could model each tooltip as an object attached with a soft spring to its black box, while simulating a strong repulsive force between all the tooltips and between a tooltip and the edge of the image. You calculate all the forces and move the tooltips iteratively, until all positions converge. You could play with making the force scale as inverse square, inverse cube, etc to find nice results.
This might be a bit of work to implement, but should probably give decent results for simple cases. It is probably impossible to guarantee that a good solution always exists, since if you add too many tooltips, your image will be full.
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:
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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)
Does anyone know a way to locate rectangles to best fit a certain area? The rectangles can be scaled up to a certain limit, but they should keep their proportions.
I basically want to rebuild Mac OS' Exposé:
Picture
Thanks,
eWolf
The problem is NP Hard, but that is only for the optimal solution. What I guess you really want is a solution that just looks good.
So I suggest looking for algorithms that make data look good. Once I wanted to layout pictures for the DeepZoom Composer and I tried to recycle a graph drawing force-interaction based algorithm. http://en.wikipedia.org/wiki/Force-based_algorithms
It worked really well even for 600 hundred rectangles, you just have to play with the details of the simulation.
How the distance is calculated?
What functions do you use for the attraction and repulsion forces?
How much overlap are you going to accept?
The only problem I could not solve entirely, was that the rectangles formed a circle shape, rather then a big rectangle shape, which is natural when you are simulating physics. But you can work around that with carefully placed auxiliary force sources.