affine | Affine transformation matrices

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Affine transformation matrices

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affine Key Features

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affine Examples and Code Snippets

Convert matrices to flat transforms .

python

Lines of Code : 31

License : Non-SPDX (Apache License 2.0)

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def matrices_to_flat_transforms(transform_matrices):
  """Converts affine matrices to `tf.contrib.image` projective transforms.

  Note that we expect matrices that map output coordinates to input coordinates.
  To convert forward transformation matr

Convert a flat transformation matrix to matrices .

python

Lines of Code : 30

License : Non-SPDX (Apache License 2.0)

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def flat_transforms_to_matrices(transforms):
  """Converts `tf.contrib.image` projective transforms to affine matrices.

  Note that the output matrices map output coordinates to input coordinates. For
  the forward transformation matrix, call `tf.li

Decrypt a message using the given key .

python

Lines of Code : 17

License : Permissive (MIT License)

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def decrypt_message(key: int, message: str) -> str:
    """
    >>> decrypt_message(4545, 'VL}p MM{I}p~{HL}Gp{vp pFsH}pxMpyxIx JHL O}F{~pvuOvF{FuF'
    ...                       '{xIp~{HL}Gi')
    'The affine cipher is a type of monoalpha

Community Discussions

Trending Discussions on affine

Padding scipy affine_transform output to show non-overlapping regions of transformed images

How to get transformation affine from ITK registration?

How to create a first-person "space flight" camera

SVG that renders differently on different OS

Reassign cell value NA in stars object

How can I save an image (nii.gz) after reshaping it?

Rasterio: writing tiff with cmap on float values

convert numpy array to 4D nifti file

How to decompose a 2x2 affine matrix with sympy?

Python given implicit equation, find points on that equation?

QUESTION

Padding scipy affine_transform output to show non-overlapping regions of transformed images

Asked 2022-Mar-28 at 11:54

I have source (src) image(s) I wish to align to a destination (dst) image using an Affine Transformation whilst retaining the full extent of both images during alignment (even the non-overlapping areas).

I am already able to calculate the Affine Transformation rotation and offset matrix, which I feed to scipy.ndimage.interpolate.affine_transform to recover the dst-aligned src image.

The problem is that, when the images are not fuly overlapping, the resultant image is cropped to only the common footprint of the two images. What I need is the full extent of both images, placed on the same pixel coordinate system. This question is almost a duplicate of this one - and the excellent answer and repository there provides this functionality for OpenCV transformations. I unfortunately need this for scipy's implementation.

Much too late, after repeatedly hitting a brick wall trying to translate the above question's answer to scipy, I came across this issue and subsequently followed to this question. The latter question did give some insight into the wonderful world of scipy's affine transformation, but I have as yet been unable to crack my particular needs.

The transformations from src to dst can have translations and rotation. I can get translations only working (an example is shown below) and I can get rotations only working (largely hacking around the below and taking inspiration from the use of the reshape argument in scipy.ndimage.interpolation.rotate). However, I am getting thoroughly lost combining the two. I have tried to calculate what should be the correct offset (see this question's answers again), but I can't get it working in all scenarios.

Translation-only working example of padded affine transformation, which follows largely this repo, explained in this answer:

...

ANSWER

Answered 2022-Mar-22 at 16:44

If you have two images that are similar (or the same) and you want to align them, you can do it using both functions rotate and shift :

Source https://stackoverflow.com/questions/71516584

QUESTION

How to get transformation affine from ITK registration?

Asked 2022-Mar-15 at 16:52

Given 3D MRI scans A, B, and C I want to perform an affine (co)registration of B onto A, take the transformation affine matrix of the registration and apply it on C.

My problem is that the affine matrix of the registration transform has the wrong signs. Maybe due to wrong orientation?

The TransformParameters contain 12 values of which the first 9 are the rotation matrix in row-major order and the last 3 are the translation values.

...

ANSWER

Answered 2022-Mar-11 at 19:38

Taking a look at this diff, you might be more interested in the old way of doing it. It directly constructs an ITK transform from 4x4 matrix.

But beware, I think there is a bug somewhere in this code. I added this recently and it decreased test accuracy, which makes me believe there is a bug somewhere in there.

Source https://stackoverflow.com/questions/71441883

QUESTION

How to create a first-person "space flight" camera

Asked 2022-Mar-15 at 13:43

I'm currently attempting to create a first-person space flight camera.

First, allow me to define what I mean by that.

Notice that I am currently using Row-Major matrices in my math library (meaning, the basis vectors in my 4x4 matrices are laid out in rows, and the affine translation part is in the fourth row). Hopefully this helps clarify the order in which I multiply my matrices.

What I have so Far

So far, I have successfully implemented a simple first-person camera view. The code for this is as follows:

...

ANSWER

Answered 2022-Mar-02 at 23:15

The problem is that two numbers, pitch and yaw, provide insufficient degrees of freedom to represent consistent free rotation behavior in space without any “horizon”. Two numbers can represent a look-direction vector but they cannot represent the third component of camera orientation, called roll (rotation about the “depth” axis of the screen). As a consequence, no matter how you implement the controls, you will find that in some orientations the camera rolls strangely, because the effect of trying to do the math with this information is that every frame the roll is picked/reconstructed based on the pitch and yaw.

The minimal solution to this is to add a roll component to your camera state. However, this approach (“Euler angles”) is both tricky to compute with and has numerical stability issues (“gimbal lock”).

Instead, you should represent your camera/player orientation as a quaternion, a mathematical structure that is good for representing arbitrary rotations. Quaternions are used somewhat like rotation matrices, but have fewer components; you'll multiply quaternions by quaternions to apply player input, and convert quaternions to matrices to render with.

It is very common for general purpose game engines to use quaternions for describing objects' rotations. I haven't personally written quaternion camera code (yet!) but I'm sure the internet contains many examples and longer explanations you can work from.

Source https://stackoverflow.com/questions/71328720

QUESTION

SVG that renders differently on different OS

Asked 2022-Mar-10 at 18:34

I'm having an issue with a svg file that renders differently on different OS. It even looks different in different editors. (Never mind the size difference below)

MacOS Safari:

Windows FileExplorer:

Linux Chrome:

I didn't create it myself. It was created on a Windows computer, in Inkscape it seems.

I wonder why it looks different? Is it possible to make it look the same, or does it need be recreated?

Here is the svg:

...

ANSWER

Answered 2022-Mar-10 at 18:34

Your screenshots indicate, that your font (Wide Latin) is installed locally on your windows desktop but not available on other systems.

You might embed the font in your svg file using a converting tool like transfonter:

Source https://stackoverflow.com/questions/71397167

QUESTION

Reassign cell value NA in stars object

Asked 2022-Mar-09 at 21:24

I recently started using the stars R package. I'm struggling with reassigning NA values to "Unknown". I found a potential solution here, but it doesn't seem to work on NAs. Any suggestions to fix this issue are greatly appreciated. for some reason SO doesn't like huge chunks of code without adding more information, so i'm adding some random text at the bottom.

Here's the code that I used:

...

ANSWER

Answered 2022-Mar-09 at 21:24

Okay actually it is very simple. Kind of cumbersome but it works like this:

Source https://stackoverflow.com/questions/71415948

QUESTION

How can I save an image (nii.gz) after reshaping it?

Asked 2022-Jan-13 at 17:14

I'm trying to reshape an image after reshaping it, I'm facing problems when it comes to the saving method. Here's the code I'm trying to run:

...

ANSWER

Answered 2022-Jan-13 at 13:26

You are trying to save a numpy array, whereas the nib.save expects a SpatialImage object.

You should convert the numpy array to a SpatialImage:

Source https://stackoverflow.com/questions/70685859

QUESTION

Rasterio: writing tiff with cmap on float values

Asked 2022-Jan-08 at 12:13

I have this very simple code:

...

ANSWER

Answered 2022-Jan-05 at 08:42

I finaly have done the trick using theses lines of code:

Source https://stackoverflow.com/questions/70573184

QUESTION

convert numpy array to 4D nifti file

Asked 2021-Dec-18 at 07:02

I am doing single-voxel simulations on python to generate simulated signals with added noise. Then, I want to convert the resulting numpy array, with the following shape (100, 100) into a nifti file.

Rows represent one simulated signal under different conditions of noise and tensor rotation. Each column represents the correspondent signal intensity for that voxel under those conditions when measured with a specific sampling scheme (100 different directions).

[DWIs array]

I am to save this matrix into a nifti file with the following format (10, 10, 1, 100).

[Desired shape]

I don’t know how to properly allocate the numpy array (DWIs.shape = (100,100)) to the format I desire (10, 10, 1, 100):

...

ANSWER

Answered 2021-Dec-18 at 07:02

In NumPy you do not need to "allocate" data arrays.

Suppose you have a 100x100 converted_array. That is

Source https://stackoverflow.com/questions/70398430

QUESTION

How to decompose a 2x2 affine matrix with sympy?

Asked 2021-Dec-16 at 15:47

I'm attempting to show the decomposition of an affine matrix with sympy as shown in the following stackexchange post:

https://math.stackexchange.com/questions/612006/decomposing-an-affine-transformation

I've setup two matrices A_params and A_matrix, where the former represents the raw matrix values and the latter is the matrix constructed from its underlying parameters.

...

ANSWER

Answered 2021-Dec-16 at 15:47

After discussion with a colleague, it turns out I made a simple error in the code. I swapped sin and cos terms. Fixing this results in the correct reconstruction of the matrix when using @Stéphane Laurent's decomposition:

Source https://stackoverflow.com/questions/70357473

QUESTION

Python given implicit equation, find points on that equation?

Asked 2021-Dec-02 at 21:42

Context: Convert an .iges to .vtk.

I have the following equation Ax^2+Bxy+Cy^2+Dx+Ey+F=0 representing a conic section.

The parameters A~F are given. I want to find points on the conic section, so that I can connect them with lines, and make a mesh.

The reason I need the points instead of just using matplotlib Ellipse is because I'm creating a mesh not a plot.

It is in 3 dimension space, but I first get points on xy plane, and use affine transformation to send it to 3 dim.

Question: How do I find points given an implicit equation?

...

ANSWER

Answered 2021-Dec-02 at 21:42

To avoid spending too much time on this, I wrote some code that seems to handle general ellipses. It can be expanded for other conics, depending on what is needed. The code takes in the coefficients of a general quadratic equation of an ellipse and a number of desired points to be generated on the ellipse and generates a set of points on the ellipse.

Source https://stackoverflow.com/questions/70148907

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