How to transform Polar to cartesian

Hi, I am a MATLAB beginner. I need the steps of how to transform polar coordinates to Cartesian. As I have 2D (jpeg)images for closed curve(organic shape an I need to convert it into an opened one. Many thanks for your help. Best regards

[Walter Roberson]

I do not think I understand how using polar coordinates to cartesian will help for the task?

Could you post a sample starting image and sample result?

http://www.mathworks.com/matlabcentral/answers/7924-where-can-i-upload-images-and-files-for-use-on-matlab-answers

[Kareeman]

Please find the link

http://www.sendspace.com/file/qoa0tu

[Kareeman]

Here is another link:

http://img97.imageshack.us/img97/315/sk1r1s.jpg

Best regards

[Kareeman]

This image is the original/starting one.and I haven't yet done any transformations.

what I need is converting the contour/curve of this image(polar coordinates) into rectangular (x,y) curve as i have a big no of images and I want to compare between them.

[Walter Roberson]

That curve "goes back on itself", and therefore cannot be a function in the polar coordinate system.

If it were in polar coordinate system, then there would have to be an origin point, but no such point is obvious. It is not clear to me, given that diagram, that choosing the centroid of the diagram would be a correct origin.

The connection to polar coordinates still escapes me.

Rather than converting polar to cartesian coordinates, are you perhaps looking to "cut" the image and "unroll" it? If so, then I am not certain you would gain anything compared to comparing it in the original space, but that would depend on how you were thinking to compare them.

[Kareeman]

Thank you very much or your reply

I see what you mean.

But the following is what i am doing:

Method B, using image processing technology

The shadow of the draped specimen is cast from below onto a white sheeting covering the top translucent lid

and centre-plates. Detailed quantitative information on the drapability of the test specimen is obtained from

digital images captured with a commercial digital camera (or a scanner) after cutting the paper around its

shadow contour. The captured images, initially having grey levels, are transformed into monochrome images

through noise filtering and thresholding. The two-dimensional monochrome images of draped shadows

described above are firstly transformed into polar (∅, r) coordinates as shown in Figure 1, where the X-axis

from 0° to 360° is the angle, in degrees, from the baseline passing through the centre of the circle, and r

(Y-axis) is the amplitude, in centimetres. The shape parameters of a two-dimensional geometric drape model

defined as the number of nodes (waves or folds), the positions of nodes, wavelength and amplitude data and

various statistical information, can then be obtained using image processing technology and frequency

analysis as well as the traditional drape coefficient. A three-dimensional drape shape can be regenerated from

its captured two-dimensional drape images, with a three-dimensional simulator.

These are the parameter I want to work out:

Calculations

10.3.1 For each test specimen diameter used, carry out separate calculations.

10.3.2 For each of the six readings on each test specimen, calculate the following, which is automatically

obtained from the evaluation software (5.3.3) (see example in Figure 5).

a) Drape coefficient, D, expressed as a percentage, using the following equation:

s d

o d

100

A A

D

A − A

−

= ×

where Ao, Ad and As are the original area of an undraped specimen, the area of a supporting plate, and

the projected shadow area of the specimen after draping, respectively.

b) Node number, one of the drape shape parameters, expressed as the number of drape waves/folds.

c) Wave amplitude, one of the drape shape parameters, indicating the size, in centimetres, of the most

dominant drape waves/folds.

d) Wavelength, one of the drape shape parameters, indicating the wavelength of the most dominant drape

waves/folds, expressed in degrees of a circle (0° to 360°).

e) Minimum amplitude, one of the statistics indicating the smallest size of drape waves/folds, expressed in

centimetres.

f) Maximum amplitude, one of the statistics indicating the largest size of drape waves/folds present,

expressed in centimetres.

g) Average amplitude, one of the statistics indicating the mean drape waves/folds present, expressed in

centimetres.

h) Variance, one of the statistics indicating the distribution of the drape waves/folds amplitude, expressed in

centimetres.

i) Fourier transform/original and dominant/original, the three fitness factors to verify the fit of the Fourier

transformation and to determine the dominant wave, expressed in percentages, using the following

equation:

f

o

Fourier transform/original 100

B

B

= ×

d

o

Dominant/original 100

B

= B ×

where Bo, Bf and Bd are the areas of the original captured draped image, its Fourier transformed shape,

and the ideal shape recomposed from a determined dominant wave, respectively, as shown in Figure 5.

j) Graph, in polar coordinates, where the X-axis (from 0° to 360°) is the wavelength, in degrees, from the

baseline passing through the centre of the centre-plate (5.1.1) and r (Y-axis) is the amplitude, in

centimetres, representing each value of the wave amplitude and the wavelength at each node.

10.3.3 Calculate the mean drape coefficient, drape shape parameters, statistics and fitness factors for face

(a) and for face (b).

10.3.4 Calculate the overall mean drape coefficient, drape shape parameters, statistics and fitness factors.

Answer 1

[Sean de Wolski]

Perhaps pol2cart?

doc pol2cart

[Kareeman]

Thanks so much for your reply.

Could you please tell me what are the steps to try it.Best Regards.

[Sean de Wolski]

type "doc pol2cart" at the command line - it'll open the documentation for pol2cart. You could probably get more specific help if you post an image (to a free webhosting website) and provide any other sample data.

Welcome to MATLAB Answers!

[Kareeman]

Thanks for your reply. I appreciate it. Could u please recommend a free webhosting website for me. Regards

[Kareeman]

I have uploaded one of the images

http://img97.imageshack.us/img97/315/sk1r1s.jpg

[Sean de Wolski]

So you want to find the coordinates of the edge of the blob?

[Kareeman]

yes

[Walter Roberson]

invert the image to make the blob white, then use http://www.mathworks.com/help/toolbox/images/ref/bwtraceboundary.html bwtraceboundary

[Kareeman]

Thanks I will try it

[Irena Chernova]

Hi Kareeman, I know that it´s not actual but I deal really with the same problem (draped samples of textile..) Could I ask you please, how did you solve it finally? Thanks a lot!