Affine transformation python example

 

If a refresher is needed, I highly  In this example, we will see how to use geometric transformations in the context of image processing. QPainter. Note that transformation matrices containing only rotations and translations are examples of rigid-body (solid-body) transformations, which do not alter the size or shape  In the spline interpolation, for example, great care was taken with the implementation of the interpolation algorithm so that everything could be expressed as a matrix Similarly, PIL provides an Image. Open up a new file, name it transform. SPECT-scan. 6 Jul 2016 This notebook presents an image augmentation method that uses both local distortion and random affine transformation. SetMatrix(img. 2  21 Jun 2014 - 2 min - Uploaded by EEEstuffMaybe a guide link? Maybe a code link? Maybe an explaination? Nope '''I made it and just 16 Nov 2016 If you are using GDAL utilities, it seems that none of them can let you > define a transformation matrix (is that confirmed?), so I believe that you > might get it through WKT2 [1] and its "Math Transform" API: > > - derive a "fitted CS" [2] with the affine transform you want to apply; > - use gdal_translate to  15 May 2009 Example: We have two affine transformations: y=A1*x+b1 and y=A2*x+b2 then the actual transformation would be: y=A2*(A1*x+b1)+b2. AFFINE—Affine transformation requires a minimum of three transformation links. ⎠. translation, scaling, rotation, shear mapping, are implemented by passing a 2x3 matrix to cv2. Transformations are cumulative within  19 Jun 2017 You need the Python Imaging Library (PIL) to use images with the ReportLab package. Fast Run-Length Encoding (Python). │. byte. To shift an image by (x,y) a transformation matrix M =[(1,0,Tx),(0,1,Ty)] using numpy array type np. The transformation filter applies an arbitrary rotation+translation transformation, represented as a 4x4 matrix, to each xyz triplet. The Symbol API, defined in the symbol (or simply sym ) package, provides neural network graphs and auto-differentiation. float32. 2 Examples  Affine Distortions. src/s/c/scikit-image-HEAD/doc/examples/plot_corner. affine_transform(input, matrix, offset=0. Translation. ⌉. dsize – size of the output image. Example. A similarity transformation is an affine transformation with isotropic scale and without shear. ⎛. Grabbing an open image. A. interpolation. 1. 1),  In this section, we will discuss about the various generalized geometrical transformations of 2D images. Affine transform is a generalization of linear transformation: Hi, I would like to calculate an affine transformation matrix from bead images (four images/channels) and apply it to many images (thousands). 3. open('example. author: Jan Bodnar website:  All input features are transformed by one of the three transformation methods: affine, similarity, and projective; each method requires a minimum number of transformation links. jpg',0) rows,cols  13 Sep 2015 Geospatial software of all varieties use an affine transform (sometimes refered to as "geotransform") to go from raster rows/columns to the x/y of the coordinate And as @Asgerpetersen pointed out, if there were a non-zero rotation parameter, the affine example would handle it seamlessly while the  1 day ago Matrices describing affine transformation of the plane. The usual way to represent an Affine Transform is by using a 2 \times 3 matrix. Map the coordinate (x, y) of an image to a new coordinate (x′,y′). Warping and affine transforms of images. The difference between two points is a . i. >>> aff = np. Notice I did a slice on the warp in this example, because I didn't need the rest of the returned values from the warp. Their locations are approximately the same as the ones depicted in the example figure (in the Theory section). A common pattern for using  The 2D pixel locations of objects in the image plane are related to their 3D world coordinates by a series of linear transformations. 0. >>> C. Most of the . 01 note lecture this in used notation. This tutorial will use the programming language Python 2. ⌈. ⌊. argmax(data, 0). Transformation can be linear or nonlinear. ⎝. 23. from matplotlib import pyplot as plt. transform. The values a through f are the first two rows of an affine transform matrix. e. 10. All image areas must have same scale, rotation, and shift. The Barnsley Fern is a fractal that can be generated using four simple affine transformations of the form: For example, the second transform will be used 85% of times, third transform 7% and so on. 2. py in our tests . For example, you can tell if gm was compiled in 16-bit mode by typing "gm version" without any options, and looking for "Q:16" in the first line of output. . qgis. TransformFeatures example 2 (stand-alone Python script). affine_transform() as an alternative affine transformation. 1 Coloring. I used Register Virtual Stack plugin and saved the tranformation parameters… you can see that, in essence, an Affine Transformation represents a relation between two images. crs {'init': u'epsg:32618'} with rasterio. eval() array([[ 2. open('clone. read_band(1)", or "help(src)" for more information. An affine transformation does not necessarily preserve  If A is a constant n x n matrix and b is a constant n-vector, then y = Ax+b defines an affine transformation from the n-vector x to the n-vector y. This set includes pure projectivities, affine transformations, perspective transformations, and euclidean  skimage. com/gingerik/qgsaffine; Latest stable version: 1. zip. The transformations modify the current affine matrix, which is initialized from the initial affine matrix defined by the -affine option. This problem . First sample %matplotlib inline # Apply transformation on image im_merge_t = elastic_transform(im_merge, im_merge. How to do perspective transformation using python and opencv | sorting out error We shall start with the traditional Euclidean transformations that do not change lengths and angle measures, followed by affine transformation. Euclidean transformations are a type of geometric transformation that preserve  2 Nov 2017 How to draw/generate the Barnsley Fern fractal in Python 3. 41 Laplace transform of a nonnegative function and the moment and. Shifting any objects location can be done using the cv2. One can specify using scipy. TRANSFORMS - Coordinate transforms in Python LINEAR2DTransfrom, A 2D affine transform. insp rasterio/tests/data/RGB. In MATLAB, 'affine' transform is defined by: [a1,b1,0;a2,b2,0;a0,b0,1] t. """ import numpy as np import matplotlib. Type in what you see on the image to the  As the above example demonstrates, in general most models evaluate array-like inputs according to the standard Numpy broadcasting rules for arrays. ⎞. Finally, we shall talk about projective For example, if you know A that transforms x to x', the matrix that transforms x' back to x is the inverse of A. 3, 1. chips> import pycrates as pyc chips> cr = pyc. Note that the translations and the rotations are defined using a 3D vector type and a quaternion type from the Eigen library. In this homework, projective and affine distortions are removed from camera images using methods different from HW#1 Now we get the affinely rectified image Xa, we want to find the affine transform matrix. Geometric operations are performed by shapely. 0, output_shape=None, output=None, order=3, mode='constant', cval=0. . The left The data is provided in the widely used Matlab format, which is also perfectly legible for Python programs through the scipy. 26 Sep 2016 how-to-perform-coordinates-affine-transformation-using-python-part-2. png. If you want a basic understanding of computer vision's underlying theory and algorithms, this hands-on introduction is the ideal place to start. Several . from skimage. A Y-shaped line feature, for example, is well modeled as a whole by a MultiLineString . Geometric . You may note  10 May 2013 This is in contrast to an affine transform, which includes scaling and shearing. For the example with Nico was there only an assumption of rotation in the x-direction? what if there was a rotation is y direction as well? Python API Guides. An Affine transformation preserves the parallelness of lines in an image. T. For example, it can crop a region of interest, scale and correct the orientation of an image. g. The library applies crops and affine transformations to images, flips some of the images horizontally, adds a bit of noise and blur and also The following example shows a large augmentation sequence containing many different augmenters, leading to sig-. circle_perimeter ) and used as a mask to extract intensity values from the image. A set C ⊆ Rn is affine if the line through any two distinct points in C lies in C,. An example would be a mask indicating the segmentation of a brain into a small number of tissue types. ,. You'll learn techniques for object recognition - Selection from Programming Computer Vision with Python [Book] We have been using the function warpAffine quite a bit over the last couple of sections, it's about time we understood what's happening underneath. QtGui. The specific transformations fall under the group known as projective transformations. It can be a useful mechanism because CNNs are not invariant to rotation and scale and more general affine transformations. If you run FreeCAD you run your own Python interpreter (Version 2. This means there is considerably less fidelity loss than when you would  affNIST is made by taking images from MNIST and applying various reasonable affine transformations to them. You can take make it into a Numpy array of type np. The data for the examples in this section can be downloaded here: ftp://ftp. mlab as mlab import  This example shows two ways how to draw an ellipse using affine transformations. 1. 5. Both scripts . T = sitk. from skimage import data. 6 Similar Modules; 7 References; 8 Information for Developers. feature import corner_harris, corner_subpix, corner_peaks. 7 Interactive Inspector (Python 2. 18 Aug 2016 aug 18, 2016 geometry image-processing geometric-transformations python numpy In this case we will apply an affine transformation to an image, mapping three points to the new origin, top right and bottom left corner. fits") chips> img = cr. There is an assumed knowledge of the core mathematical concepts in matrices and vectors. tif', 'w', **src. The following class members are part of the Qt 3 support layer. 0. 33. Example 3. 2. 1 Key MRML nodes; 8. = │. cxx In that program use first a large number of bins (for example 2000) and identify the In your case, for an Affine Transform in 2D, you have 6 parameters. resampler = sitk. 2 Affine sets. example. write(src. 2 Using an Affine Transformation on a Range of Vertices. = b. There are a variety of constructors available for Affine objects. ⌋. loadmat function. transformation matrix. imread('messi5. array([[1,2,3],[2,3,4],[4,5,6],[6,7,8]]) >>> apply_affine(aff, pts) array([[14, 14, 24], [16, . shape[1] * 2, . 236 seconds). 10 Nov 2010 For example, go to "File - Open Samples - Boats (356K)". In computer graphics people deal Read More →. We want to get scanner RAS+ coordinates corresponding to the voxel coordinates. GeoPandas extends the datatypes used by pandas to allow spatial operations on geometric types. read_file("img. 0, prefilter=True)[source]¶. py scikit-image(Download) ? python code examples for SimpleITK. Normalizes layer outputs for every minibatch for each output (feature) independently and applies affine transformation to preserve representation of the layer. 05 mod = AffineTransformationModifier( transform_particles = True, transform_box = True, transformation  Example. This page provides Python code examples for skimage. 25 Aug 2014 In that post I mentioned how you could use a perspective transform to obtain a top-down, “birds eye view” of an image — provided that you could find So let's not waste any more time. 27 Jun 2016 Note: There is of course numerical error here, and this may not be the best way to solve for the transform (you might be able to do some sort of least squares thing). jpg. More Details. First, a usage example: 7 Jul 2017 Get a filename for an example file: In that case the Coordinate System may well have an affine property which returns the affine matrix corresponding to the transform. GetDirection()). astype(dtype = int ). ResampleImageFilter(). Translation, rotation, and scaling are all examples of affine warps. The affine transformations described so far will generate purely rigid-body mappings. INTER_LINEAR. Author: Mauricio de Paulo and Erik Timmers; Maintainer: mauriciodev; Owners: gingerik; Plugin home page: http://plugins. For such an image, one does not  The following Python function finds, by least squares fitting, an affine transformation that (approximately) transforms given set of points/vertices/vectors (from_pts) to another (to_pts). In the process, the Here are some examples. from soma import aims, aimsalgo >>> import math >>> vol = aims. 1 Problem. name", "src. Let R be a transformation matrix  15 Mar 2007 3) Number of histogram bins: First plot the histogram of your image using the example program in Insight/Examples/Statistics/ImageHistogram2. Examples of the techniques below can be found by running the script test_pdfgen_general. We have been using the function warpAffine quite a bit over the last couple of sections, it's about time we understood what's happening underneath. hough_circle ) providing the drop radius and its center. AffineTransformation2D ([matrix, translation]), Perform an affine transformation in 2 dimensions. It allows you to compose a bunch of affine transform objects into a single transform, which means you can do many different kinds of augmentation (and downsampling) in a single resampling step. With. get_transform("eqpos") chips> (yi, xi) = np. Mutual Information  8 Mar 2018 OpenCV (i. where(img  2- Translation Transformation; 3- Rotation Transformation; 4- Scaling Transformation; 5- Shearing Transformation; 6- Affine Transformation; 7- Combination of transformations. You'll have to consider whether this is acceptable or  you can create the transformation matrix \textbf{M} as follows: M = \begin{bmatrix} 1 & 0 & t_x \\ 0 &. Example: from ovito. visible. 3 Homographies and Transformation Matrices. In portfolio optimization, for example, we seek the best way to invest some 2. /. 2 Transform display options. • In homogeneous coordinates, 3D affine transformations are represented by 4x4 matrices: •A point transformation is performed: 1. 4 Affine is any transformation on any given input image that preserves parallel lines and distance ratios between points on a straight line in the source image. /_images/sphx_glr_plot_features_001. In this tutorial we will see how to warp a single triangle in an image to another triangle in a different image. 2 Jan 2015 Here, we visualise matrix linear and affine transformations to set the foundation in understanding more awesome computer vision techniques (still a learning process for me). Tensor Transformations · Asserts and boolean checks · Running Graphs · Constants, Sequences, and Random Values · BayesFlow Monte cosine_decay · cosine_decay_restarts · create_global_step · do_quantize_training_on_graphdef · Example · ExponentialMovingAverage · exponential_decay  31 Dec 2013 Affine Transformations; Other Transformations; Other Operations. The given matrix and offset are used to find for each point in the output the corresponding coordinates in the input by an affine  In geometry, an affine transformation, affine map or an affinity is a function between affine spaces which preserves points, straight lines and planes. float32 and pass it into cv2. Therefore, it finds a similarity transformation rather than a general affine transform. For example, it is trivial to create the simplest Affine transform, the identity transform:. cea. #we rotate the image according to its transformation using the direction and according to the final spacing we want newSize = newSize. python code examples for PyQt5. l t thiid t ti. There are some important special cases of these projective transformations. In Chapter 5, we propose a  GeoPandas is an open source project to make working with geospatial data in python easier. from __future__ import Basics¶. 7. Apply an affine transformation. >>> # create 3x2 matrix in a sequence of length 1 in a batch of one sample >>> data = [[10, 20],[30, 40],[50, 60]]. It works with arbitrary dimensional points and requires at least dim points, when your points are dim-dimensional. Repeating the process on each  3D Point Representation. Scale change  Image warping. 1 Matrices and Matrix  This algorithm uses an affine transformation as opposed to a polynomial geometrical transformation, which by default is skimage. 1 Transform editing and application; 5. The two transformations use different algorithms and thus do not  The MI registration criterion states that the images are geometrically aligned when MI(A,B) is maximal. import cv2 import numpy as np img = cv2. , . io. transform( ) function which very quickly applies an affine transform to an image, based on the values (a, b, c, d, e, f). 1 An example where the loss remains the same regardless of the rotation but neither the domain points x1, ready algorithm written in Python for readability. The reproject() function takes source and destination ndarrays and an affine transformation vector and coordinate reference system for each. Note Example¶. If we know the MRI intensities, the uncertainty of the SPECT intensities is minimal when the scans are aligned. org/plugins/qgsAffine; Tracker: Browse and report bugs; Code repository: https://github. nii') >>> # create an affine transformation matrix >>> # rotating pi/8 along z axis >>> tr . 5 1 0; 0 0 1]);. Rong Zhang. Optimization Algorithms: Forward Additive, Forward/Inverse  25 Feb 2014 rasterio. The following example converts an RGB image (linearly calibrated according to ITU-R 709, using the D65 luminant) to the CIE XYZ colour space: . Furthermore all drawn elements are passed through an affine transformation which may adjust their. 32. Then, a smaller concentric circle is drawn ( draw. tif') as src: with rasterio. Affine Image Alignment. QtGui. matlab. A symbol represents a multi-output symbolic expression. The filter does no checking to ensure the matrix is a valid affine transformation — buyer beware. So what the script does is create a base based on three selected points and then constructs a matrix for an affine transformation, which can be used to transform points in space. read('data_for_anatomist/subject01/subject01. • A 3D point P is represented in homogeneous coordinates by a 4-dimensional vector: •As for 2D points: 1 z y x. Merging The first premise of Shapely is that Python programmers should be able to perform PostGIS type geometry operations outside of an RDBMS. Antialiasing QPaintEngine provides the interface that the painter uses to draw onto different types of devices. For all other cases, we will typically use rows to store data, for example features for clustering and classification. 5), but it also use the in addition libs of an other installed The topic describes how affine spatial transformation matrices are used to represent the orientation and position of a coordinate system within a "world" . Models can therefore already be Base class for HEALPix projections. fr/pub/dsv/anatomist/data/demo_data. AffineTransform. We start by telling the opened Script Editor what language you want to write the script on: choose "Language - Python". 29 Oct 2013 I am trying to wrap my head around the transformation matrix in Rhino Python, and was wondering if there was something out there that listed what each item in the For example, certain scale operations rotation operations can cause the scale and rotation components of the transform will become mixed. Zooms. One of the best We need the latest version of PyTorch that contains affine_grid and grid_sample modules. Also, the error for converting primary_systemx to secondary_systemx is (for this example) of order 10^(-2). The first two columns of the matrix encode scaling, rotation and shear and the last column the translation. get_image(). 22. Before talking about affine transformations, let's learn what Euclidean transformations are. We have voxel coordinates (in voxel space). 4. Filed Under: how-to, Tutorial Tagged With: affine transform, fillConvexPoly, triangle  21 Jul 2014 The default interpolation function is cv2. Figure 5: sample. 3 Zooms. array([[0,2,0,10],[3,0,0,11],[0,0,4,12],[0,0,0,1]]) >>> pts = np. NxM transform matrix in homogeneous coordinates representing an affine transformation from an (N-1)-dimensional space to an (M-1)-dimensional space. warp() . Qt 3 Support Members for QPainter. 10  17 May 2016 Keywords: multi-touch gestures, affine transformation, similarity, rigid body, direct manipulation, pattern recognition . For example, a rotation about the first axis of π/2 radians followed by an equivalent rotation about the second would produce a very different result to that obtained if the order of the operations was reversed. 5) Type "src. An affine transformation ⎡ ⎣ x y 1 ⎤ ⎦ = ⎡ ⎣ a 1 a 2 t x a3 a4 ty 0  The affine matrix as a transformation between spaces¶. So, what I have . Geometric  2 Sep 2012 An affine transform is composed of zero or more linear transformations (rotation, scaling or shear) and translation (shift). “+”), or a neural network layer (e. 18 May 2016 Warp one triangle to another using OpenCV ( C++ / Python ). tform = AffineTransform(scale=(1. It is defined by the transformation matrix Learn data science in Python with a mentor. Examples. Python, shapely library: is it possible to do an affine operation on shape polygon? Shapely's affinity module supports affine transformations on any geometry, for example: from shapely import affinity from shapely. AffineTransform( 3 ). In the current version of PIL, the method argument can be EXTENT (cut out a rectangular subregion), AFFINE (affine transform), QUAD (map a quadrilateral to a rectangle),  7 May 2012 In this post I give an example on how to use my first R package, called 'vec2dtransf', for applying similarity and affine transformations on vector da This format makes matrix multiplications and point transforms easier. ndimage. cv2 must be available in python). This function, paired with the information that it is a map from atlas-voxel to subject-voxel is another example of a Coordinate Map. warpAffine() function. Geopandas further depends on fiona for file access and descartes and matplotlib  2 Jun 2017 A good example and introduction can be found in the matrix example program. 5. py. OpenCV getPerspectiveTransform Example. get_transform("sky") chips> eqpos = cr. A mapping h: P2→P2 is a homography if and only if there exist a non-singular 3x3 matrix H such that for any point in P2 represented by a vector x it is true that h(x)=Hx. tform = fitgeotrans( movingPoints , fixedPoints , transformationType ) takes the pairs of control points, movingPoints and fixedPoints , and uses them to infer the geometric transformation specified Type of transformation, specified as one of the following: 'nonreflectivesimilarity' , 'similarity' , 'affine' , or 'projective' . array in the first example would be used once the coefficients of the affine array were determined. Antialiasing Together with the QPaintDevice and QPaintEngine classes, QPainter form the basis for Qt's paint system. 3. The image (source) we are going to use in this example is this one: Loading the  Horizontal Shear Example tform = maketform('affine' [1 0 0; 5 1 0; 0 0 1]); tform maketform( affine ,[1 0 0; . how to render the Barnsley Fern in Python 3. See below example for a shift of (100,50):. 4. In variant 1, we tell PyX to apply a couple of affine transformations before stroking this circle on the canvas c . P z y x z y x p. In this example, we use the functions translate() and rotate() on a range of control vertices. In general, we have some voxel space  20 Feb 2013 The Python Imaging Library (PIL) allows you to create, modify, and convert image files in a wide variety of formats For example, drawing an ellipse inside the bounding box (0,0,5,10) will produce an ellipse 5 pixels wide and 10 . values chips> sky = cr. OpenCV Perspective Transform. The Transformations example shows how of QPainter's coordinate system. read()). flags – combination of interpolation methods (INTER_LINEAR or INTER_NEAREST) and the optional flag WARP_INVERSE_MAP, that sets M as the . • For example, let A be an MRI-scan and B a. profile) as dst: dst. scipy. Master machine learning and advanced data science topics, with To give you visual examples, consider the image. Several different geometric transformation types are supported: similarity, affine, projective and polynomial. Learn how to use python api PyQt5. Download Python source code: plot_geometric. The contact line is detected by a circular Hough transform ( transform. >>> src. 1 Introduction and Acknowledgements; 2 Module Description; 3 Use Cases; 4 Tutorials; 5 Panels and their use. tif Rasterio 0. Limitations: Image shapes must be equal and square. An operator can  Linear Algebra Video Lectures, The University of New South Wales Online Course, free tutorials for free download Affine transformations are typically used instead because only affine The scale-invariant feature transform (SIFT) is an Python function to find an approximate affine transformation, given to sets of points. HW2 Report. An Affine Image Alignment algorithm aims to find the optimal alignment between an input image and a template image with respect to the parameters of an affine transform. Affine transformations, i. The following example code shifts the image by (200,100). warpAffine. All Samples(61) | Call(47) | Derive(0) | Import(14). More than 27 million people use GitHub to discover, fork, and contribute to over 80 million projects. Affine Transformations. This is a routine that takes in two sets of points and finds the best affine transformation that maps between them. Shares Example, there are two rectangles in the same position and size, we will use the Translation Transformation to move the second rectangle. We need a coordinate transform to take us from voxel coordinates to scanner RAS+ coordinates. They are composited by operators, such as simple matrix operations (e. The method that is implemented in menpofit is: Lucas-Kanade (LK). resampler. #!/usr/bin/python ''' ZetCode PyCairo tutorial This is a star example which demonstrates scaling, translating and rotating operations in PyCairo. It is typical to use an alternate constructor to create affine transforms, rather that the default constructor. , if for any x1, x2 ∈ C and θ ∈ R, we have θx1 + (1−θ)x2 ∈ C. Demonstrates how affine transformations in QPainter works. I've also done a Python version (still learning the language). Theorem: Definition: Homography. py, and let's get started. 8 Feb 2018 [hide]. To get back to the example in the first post: I can then use the length of a vector of two points of the square to stretch the arch so it  The Barnsley Fern is a fractal which resembles the Black Spleenwort species of fern. QPainter can  3. Example of a translation by 100 pixels in x and y: rows, columns  Definition 2. Before talking about affine transformations, let's see what Euclidean  10 Aug 2011 Although there is nothing special about it, but, strangely, I could not find it in GDAL-python (though it is very good library for working with raster and shape files, and I like it), also I looked at another respected library - shapely, but unfortunately, there is no capability to move, rotate or translate the shapes (but  Operations that modify a transform always return a new transform object. GitHub is where people build software. It is constructed by plotting a sequence of points in the $(x,y)$ plane, starting at $(0,0)$, generated by the following affine transformations $f_1$, $f_2$, $f_3$, and $f_4$ where each transformation is applied to the previous point and  A dataset has a coordinate reference system and an affine transformation matrix that maps pixel coordinates to coordinates in that reference system. Example: Align two images and combine them to produce a larger one. geometry import LineString # Example geometry line = LineString([(1, 3), (1, 1), (4, 1)]) # Rotate 30 degrees  Affine transform of an image ============================ For the backends that support draw_image with optional affine transform (e. An Affine transform can be (the following  This class makes it possible to implement new modifier types in Python which can participate in OVITO's data pipeline system and which may be used like OVITO's . transform import warp, AffineTransform. , agg, ps backend), the image of the output should have its boundary match the dashed yellow rectangle. The affine transform consists of six coefficients returned by GDALDataset::GetGeoTransform() which map pixel/line coordinates into georeferenced space using the When the dataset is a covariance matrix, for example, this metadata item will be one of Covariance_11, Covariance_22, Covariance_33, Covariance_12,  scikit-image is great for this. modifiers import * xy_shear = 0. In order to create an ellipse, we best start from a unit circle centered around the point of origin of the coordinate system (here: circ ). This example rotates the points around the z-axis while translating them. Also, sets of parallel lines remain parallel after an affine transformation. 3D Geometrical Transformations. Transform an image to align its pixels with those in another image. But in the compact representation this is . H2 = ( ECE661. 31. Python. A = \begin{bmatrix} . Transformation parameters are: isotropic scale factor, rotation angle (in degrees), and translation vector. warpAffine . 8. convolution layer)