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Hereby the reflection of a light pattern is observed by a camera. The distortion of the reflected pattern is evaluated to obtain information about the reflecting surface.
Next..In Tarini method, it requires the color matte pattern to be projected in the specular surface. We generate the pattern using MATLAB function. This figure shows one period of the matte. It is built from hat function from three different color (RGB) overlapping in the middle of the peak intensity. The image result shown in here, which gives a gradual increase and decrase of intensity in each color....To obtain a complete matte, we duplicate this unit matte in row and column
From this repetition, we get 4 patterns of matte. In vertical pattern,we repeat this unit matte 5 times in order to construct a good resolution in the monitor. Then, it is oriented by 90 deg to get horizontal pattern, 45 and 135 to get all of the complete set of matte.
So, we began our experiment using the object which has a flat specular surface with a ridge contour. We send a white and 4 pattern from the monitor to our specular object.white image values are used to normalize perceived RGB so that it is robust to color shifts.Then, we captured these 4 images.We changed the position and orientation of the object in order to measure the depth. In each position, one set of image (white and 4 projected matte pattern) is acquired. Unfortunately, the quality of different projected patterns in the object is not very good due to the non-perfect reflectivity of the object.. Thus, we decided not to use this object
We changed into a perfect mirror as our specular object, to get a perfect reflectivity. We project matte pattern and captured these images in the same way as the previous procedure. In this matting capture, we infer that it requires 4 images and each point is independent from neighbors..which is an important property for reconstruction.Then, we can proceed to the next step...
Next, we wish to reveal the true location of the object surface. First, we must do the matte extraction to deduce data from the received pattern. According to Tarini method, we can get the 6 regions from this graph that can be useful to determine the location of real pixel in the monitor. As we know, this graph is one periodic of our matte pattern. This repeated period of the stripes is perceived by the camera as the periodic function. For each pixel,we can get 4 color values from 4 images (c). X is the position inside one stripe for each matte pattern. We success to determine this x, using this equation..Then, by solving this equations using Diophantine method, we should get y1..4or in which stripe this pixel belong to in the pattern.Unfortunately, we cannot achieve this – y so we cannot proceed to get the true depth and geometric reconstruction.
Because we could not solve this problem, we change the method into…
We need to setup our experiment again. At the beginning, we must set the most optimum exposure time, by projecting the 1 unit matte to the mirror. Then, we extract one line of the cropped image to get the curve. We can see that it has a clipped peak caused by saturation
Therfore, we should adjust the exposure time and camera setting so that now the curve should not give a saturated peak like this..
Because the color projected by the monitor is not matched with the intensity perceived by the camera, we must do color calibration step. To calibrate it, weshould get a response curve by displaying a linear ramp for each color channel varying from 0 to the maximal value. We generate this ramp using MATLAB, so that we get this red ramp… grenen.. Blue..
These ramp images are projected to mirror object and captured by the camera
We extract one line from these images so we can generate the response curve of each color ramp from what camera perceived.As an example, when we projected the Red ramp, the curve from the Red channel gives a linear response but there are responses also from Green and Blue channels. This is also the case for the Green and Blue ramp.
But, we only considerthe linear relation between the original ramp pattern and the perceived color. Knowing the linear response curve in Red, Green and Blue channel, we can find the minimum and maximum values of perceived color in each channel...as displayed by in this table.
These values are used to normalize the color in the captured images to get a more accurate calculation. Now, the intensity in Red, Green and Blue are displayed in almost the same range [0 255].
The experimental setup for our project is shown in the figure. We rotate our specular object which is mirror 1 degree at a time. Theta will increment 1 degree everytime we captured the mirror until the it reach the monitor edge. That is until there is no pattern on the mirror. We calculate the distance between the camera and the mirror, d by using hypothenus of the triangle with the measurement we made.When the theta is 1 degree (that is when the mirror increment 1 degree), the pattern captured is shift by delta. We want to find the relationship between the changes in the shift, delta with theta. The changes of the shift, delta is a function of alpha by the formula shown here using the trigonometric identity.By rearranging the formula, we can get the delta in terms of alpha.So, what is the relationship between alpha with theta?
We project the vertical pattern on the monitor instead of diagonal pattern for maximum shift observation. Figure on the top left show the mirror at 0 degree, 2nd figure on top row show mirror at 2 degree, 3 degree and so on. It can be seen clearly that the pattern on the pattern is shifted. For example, the blue stripe on first image goes to the left and the red stripe comes and then green stripe & so on. In order to analyse the pattern shift, we extracted one line from the middle of the mirror and plot the color curve as previously mentioned.
All the color curve for all the angle theta is plotted.From these curve, we have to find the the shift of the curve. We compute the shift by taking the peak of R, G, and B curve as a correspond point.So, we find the position of these peak in subsequent image to find the shift between these points.We record the shift of the peak of R, G, and B in the table.
The table shows the theta Vs the shift in R, G, and B.From the table, we couldn’t find a relationship between the theta & the shift directly. Let us look again our colour curve for finding this relationship.
We see that from the graph, some peak are distorted which will make the calculation of shift not so accurate. And, let us consider only the peak that are in better condition.Let’s see the first two image, the Red peak appear good in both image. And how about in 2nd and 3rd image, the Red peak seems distorted. So, let’s consider Green peak in 2nd and 3rd image. Green peak seems good. How about 3rd and 4th image, Blue seems fine. So, in this way, by considering the different peak shift in different color curve sequences, we can get a better relationship between the theta and the shift. We recorded these data in the following table.
The table shows the relationship between the theta and the shift by considering different colour peak during different colour curve sequence. From these data, we found out that the increment of 1 degree in theta has a constant shift in delta.And this hold true for the relationship between theta and alpha.We conclude that increment in theta of 1 degree has a constant alpha.
Hence, we found out that the angle shift relationship is as follow: the increment of 1 degree in theta gives a constant alpha which is 1.7 radian which is corresponds to delta equal to 97 pixel.
. In our project we tried the Tarini method using four matte patterns and specular objects, but it was not successful in extracting the matte.
Shape from Distortion - 3D Digitization
BY:Agam A. NugrohoVanya V.Valindria Eng Wei Yong VIBOT 4 2011
3D image reconstruction main issues in computer vision. Many technique: Shading Texture Stereoscopy Structured Light Contour Shape from distortion reconstruct the 3D shape of the mirror from its reflected images
Obtain the relationship that is useful in 3D surface reconstruction for specular objects. 3D surface normal map depth map
Deduce 3D shape of the target object by looking at the way it distorts patterns from a monitor.
This method works by measuring a surfaceslope of an optical beam which is deflected bythe surface.
3D reconstruction of specular surface can be performed using shape from distortion method In this project, we succeed to obtain the orientation-shift relationship using the flat surface This result will be useful for extracting the depth from the specular surface In the future it can be extend to a more complex shiny surface 3D reconstruction.
M.Tarini, et,al, 3D acquisition of mirroring objects using striped patterns, Graphical Models 67 233–259.2005. Hui-Liang Shen, et.al. Estimation of Optoelectronic Conversion Functions of Imaging Devices Without Using Gray Samples, Wiley Periodical. Volume 33, Number 2, April 2008. V. Hanta. SOLUTION OF SIMPLE DIOPHANTINE EQUATIONS BY MEANS OF MATLAB. Institute of Chemical Technology, Prague. Y. Francken. Metostructure Acquisition with Planar Illuminants.PhD Dissertation. University of Maastrich