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Affine Transformation
Published in Ravishankar Chityala, Sridevi Pudipeddi, Image Processing and Acquisition using Python, 2020
Ravishankar Chityala, Sridevi Pudipeddi
An affine transformation is a geometric transformation that preserves points, lines and planes. It satisfies the following conditions: Collinearity: Points which lie on a line before the transformation continue to lie on the line after the transformation.Parallelism: Parallel lines will continue to be parallel after the transformation.Convexity: A convex set will continue to be convex after the transformation.Ratios of parallel line segments: The ratio of the length of parallel line segments will continue to be the same after transformation.
Geometric Transformation Techniques
Published in Jyotismita Chaki, Nilanjan Dey, A Beginner's Guide to Image Preprocessing Techniques, 2018
Jyotismita Chaki, Nilanjan Dey
Geometric transformation is actually the rearrangement of pixels of the image. Coordinates of the input image is transformed into the coordinates of the output image using some transformation function. The output pixel intensity of a specified pixel position may not depend on the pixel intensity of that particular input pixel, but is dependent on the position as specified in the transformation matrix. There are two types of geometric transformation: pixel coordinate transformation and brightness interpolation. Pixel coordinate transformation, or spatial transformation, of an image is a geometric transformation of the image coordinate system, that is, the mapping of one coordinate system onto another. Mapping can be forward (map pixels of an input image onto an output image) or backward (map pixels of an output image onto an input image). This type of transformation involves some linear mapping like translation, scaling, rotation, shearing, and affine transformation. Nonlinear mapping involves twirl, ripple, and spherical transformation. The brightness interpolation is generally done by defining the brightness of the original pixel in the input image that resembles the pixel in the output discrete raster image. Brightness interpolation involves nearest neighbor interpolation, bilinear interpolation, and bicubic interpolation.
Geometry operations
Published in Robin Lovelace, Jakub Nowosad, Jannes Muenchow, Geocomputation with R, 2019
Robin Lovelace, Jakub Nowosad, Jannes Muenchow
Affine transformation is any transformation that preserves lines and parallelism. However, angles or length are not necessarily preserved. Affine transformations include, among others, shifting (translation), scaling and rotation. Additionally, it is possible to use any combination of these. Affine transformations are an essential part of geocomputation. For example, shifting is needed for labels placement, scaling is used in non-contiguous area cartograms (see Section 8.6), and many affine transformations are applied when reprojecting or improving the geometry that was created based on a distorted or wrongly projected map. The sf package implements affine transformation for objects of classes sfg and sfc.
Recognition of expiry data on food packages based on improved DBNet
Published in Connection Science, 2023
Jishi Zheng, Junhui Li, Zhigang Ding, Linghua Kong, Qingqiang Chen
The affine transformation is a linear transformation from two-dimensional coordinates to two-dimensional coordinates, maintaining the “straightness” and “parallelness” of the graph. The affine transformation allows you to translate and rotate the image. The transformation rule calculates a transformation matrix from the four predicted coordinate points on the original image and the corresponding preset position coordinates, and then transforms the original image into a new image by the transformation matrix. The affine transformation can be expressed by Equation (4). where (tx, ty) represents the amount of translation, while the parameter reflects ai the changes in image rotation, scaling, etc.
DeepMorpher: deep learning-based design space dimensionality reduction for shape optimisation
Published in Journal of Engineering Design, 2023
Asad Abbas, Ashkan Rafiee, Max Haase
Our proposed PointNet-based encoder is shown in Figure 1 and consists of three main components. The transformation network (red colour), shared multi-layer perceptron (MLP) network (orange colour) and max-pooling layer (green colour). In the first step, to make learned representation invariant to certain transformations, such as rotation and translation, a spatial transform matrix forming a mini-network is used. Input transformation network directly applies affine transformations to the coordinates of input points and transforms the input features into a canonical representation. The input transformation mini-network contains three main sub-networks, namely, point-independent feature extraction, max-pooling and fully connected layers. Furthermore, a second transformation network (feature transformation network) is used for the alignment of feature space from different input point clouds. However, the transformation matrix in the feature space has a much higher dimension than the spatial transform matrix in the input transformation network. After feature transformation, an MLP network followed by a max-pooling layer is used to aggregate point features. The size of the last fully connected layer, prior to max-pooling, controls the dimensions Z of latent space.
Effective detection of COVID-19 outbreak in chest X-Rays using fusionnet model
Published in The Imaging Science Journal, 2022
Ganesh Keshaorao Yenurkar, Sandip Mal
The data augmentation process is carried out in the proposed FusionNet model to maximize the data size. The augmentation approaches like cropping, flipping, zooming and rotation are performed in the proposed model to generate a balanced dataset. Deep for a reliable classification outcome, But in the case of some efficient datasets, the data size may not be sufficient, so data augmentation techniques are employed. Especially in the case of images, the augmentation techniques, including scaling, cropping, padding, rotation, flipping, translation and affine transformation, are generally carried. In image scaling, the input mages are resized over a particular range, whereas the width can be doubled. Cropping is carried out to grab only the particular image portion and leave behind the unwanted portions. Flipping is nothing but the transition of horizontal or vertical flips. The images are padded based on the defined set of values towards all sides during padding. In rotation, the angles of images can be randomly considered, and during translation, the images can be moved either on the x-axis or y-axis. During affine transformation, the straight lines, planes and points of images can be preserved. The data augmentation process not only maximizes the data size but also avoids overfitting issues, so the generalized model could be better.