Add Gaussian Noise To Image Python Numpy

Function to add random noise of various types to a floating-point image. You could also generate the linear SNR from your SNR in decibels, I've used this function in one of my projects once:. Because of this limitation of integer. Almost all image processing tools today, provides features on histogram. The sharp change is edge. Following is a simple program to verify the OpenCV Python package. gaussian_filter taken from open source projects. Parameters image ndarray. NumPy is the fundamental package for scientific computing in Python [NumPy Reference] Matplotlib is one of many plotting packages. This is what we are going to do in this section. misc import imsave. As I mentioned earlier, this is possible only with numpy. the parameter sigma will be used to vary the amount of noise to be added. Keywords: ComputerVision,OpenCV,SciPy,NumPy 1 Introduction. This is also image addition, but different weights are given to images so that it gives a feeling of blending or transparency. layers import Conv2D, MaxPooling2D from keras import backend as K import numpy as np import pescador batch_size = 128 num_classes = 10 epochs = 12. uneven illumination). import scipy. 0] like this. Multiplying an image by a noise image generated from a Gaussian function effectively changes the standard deviation of the pixel values. Thus, by randomly inserting some values in an image, we can reproduce any noise pattern. Sekarang kita belajar tentang image filtering dengan menggunakan library opencv di python. The Gaussian distribution is symmetric about the mean of the probability. If PCH is true, then the sampled values may be different per channel (and pixel). There are many applications for taking fourier transforms of images (noise filtering, searching for small structures in diffuse galaxies, etc. In this tutorial, you will discover white noise time series with Python. sensor noise caused by poor illumination and/or high temperature, and/or transmission eg. #This source code is public domain #Author: Christian Schirm import numpy, scipy. We are jumping from one package to the next, calling mahotas to filter the image and to compute the threshold, using numpy operations to create a thresholded images, and pylab to display it, but everyone works with numpy arrays. Write the source code below. normal (loc=0. Since derivative filters are very sensitive to noise, it is common to smooth the image (e. The visual effect of this blurring technique is a smooth blur. # Add noise image. The cut_off_point is also set to 15 because an average ROI intensity above that means that the ROI is mostly white, while an average ROI intensity below that means the ROI is mostly black. Many high quality online tutorials, courses, and books are available to get started with NumPy. Here I used MATLAB function ‘randint’. util import random_noise im = random_noise(im, var=0. Performing Fits and Analyzing Outputs¶. ContrastNormalization ((0. Laplacian of Gaussian + 2d Gaussian fit. This is Distribution is also known as Bell Curve because of its characteristics shape. import numpy as np. A function to compute this Gaussian for arbitrary \(x\) and \(o\) is also available ( gauss_spline). 1)Image dimensions, but those are given, so I take that on trust 2)The difference that allow me to add Gaussian noise in right way is that '*' before 'uint8'. Image Blurring (Image Smoothing) Image blurring is achieved by convolving the image with a low-pass filter kernel. With just a few lines of code, you will convert RGB images to grayscale, get data from them, obtain histograms containing very useful information, and separate objects from the background!. normal¶ numpy. In those techniques, we took a small neighbourhood around a pixel and did some operations like gaussian weighted average, median of the values etc to replace the. To run the examples, be sure to import numpy in your session. You can add several builtin noise patterns, such as Gaussian, salt and pepper, Poisson, speckle, etc. I want to test the code with a given signal to noise ratios (SNR). I've attempted to do this with scipy. An order of 0 corresponds to convolution with a Gaussian kernel. One of the common technique is using Gaussian filter (Gf) for image blurring. First convert the RGB image into grayscale image. Computing an average image from a list of images is not difficult. In this OpenCV with Python tutorial, we're going to be covering how to try to eliminate noise from our filters, like simple thresholds or even a specific color filter like we had before: As you can see, we have a lot of black dots where we'd prefer red, and a lot of other colored dots scattered. 607 times its maximum at and [R255] ). Finds Intensity Gradient of the Image. 7, anaconda's default packages are unfortunately unsuitable because they require an ancient compiler which is unable to compile VIGRA. by changing the 'mode' argument. The NumPy module uses a machine's natural number types to represent the data values, so a NumPy array can consist of integers that are 8-bits, 16-bits, and 32-bits. Python was created out of the slime and mud left after the great flood. Sedangkan noise salt & pepper seperti halnya taburan garam, akan memberikan warna putih pada titik yang terkena noise. The visual effect of this blurring technique is a smooth blur. Moreover, as shown in the image below, which displays the tracking scenario of this demonstration, it is possible that in some frames no location can be determined. OpenCV package for Python is successfully installed. Explore the mathematical computations and algorithms for image processing using popular Python tools and frameworks. Add the processed data for this slice into a NumPy ndarray of processed data. Will be converted to float. Started as a Matlab clone. The underlying implementation in C is both fast and threadsafe. Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately. I'm trying to add gaussian noise to some images using the following code import numpy as np import cv2 import glob mean = 0 var = 10 sigma = var ** 0. 5 can be downloaded via the anaconda package manager. , noise_sigma, input. from random import gauss x=[gauss(mu, sigma) for i in range(10000)] for which in the last line I used the "pythonic" condensed version of a for loop, the list comprehension. PDF | An introduction to computer vision in Python, from the general concept to its implementa-tion with some current open-source libraries. Without further ado, let's blur an image in Java. The encoding process repeats the following: multiply the current total by 17 add a value (a = 1, b = 2, , z = 26) for the next letter to the total So at. DLLs directory. With just a few lines of code, you will convert RGB images to grayscale, get data from them, obtain histograms containing very useful information, and separate objects from the background!. Join us in building a kind, collaborative learning community via our updated Code of Conduct. Utilizes the Python Imaging Library, and is an example of the usage of this library. For creating a transparent image you need a 4 channel matrix, 3 of which would represent RGB colors and the 4th channel would represent Alpha channel, To create a transparent image, you can ignore the RGB values and directly set the alpha channel. Image stacking using python is fast, efficient, and allows for custom filtering during the stacking process. by changing the ‘mode’ argument. Some of the operations covered by this tutorial may be useful for other kinds of multidimensional array processing than image processing. In OpenCV, image smoothing (also called blurring) could be done in many ways. How to add noise (Gaussian / salt and pepper, etc. From Google Maps and heightmaps to 3D Terrain - 3D Map Generator Terrain - Photoshop - Duration: 11:35. kernel의 사이즈는 양수이면서 홀수로 지정을 해야 합니다. Input image data. Matplotlib also able to create simple plots with just a few commands and along with limited 3D graphic support. Median Blur can be used to minimize noise effects on the image. imread("pyimg. There are two types of noise that can be present in an image: speckle noise and salt-and-pepper noise. Legal Notice. Since each value can have 256 different intensity or brightness value, it makes 16. Does anybody have a recipe for adding noise to a raster using python (possibly with GDAL/Numpy/PIL/or something else). We will begin by considering additive noise with a Gaussian distribution. datasets import mnist from keras. As part of our short course on Python for Physics and Astronomy we will look at the capabilities of the NumPy, SciPy and SciKits packages. Utilizes the Python Imaging Library, and is an example of the usage of this library. The noise comes from the normal distribution N(L,S). but the problem is that the noisy image show only noise, and not the original image with noise added. Bounds and weights are supported. How to de-noise images in Python How to install Ubuntu 16. To smoothe noise and the edges, we use a Gaussian filter:. Python’s os, secrets, and uuid modules contain functions for generating cryptographically secure objects. pyplot as plt from scipy. To run the examples, be sure to import numpy in your session. If you only want to add some random noise to your data, you could add a normal random sample with a small standard deviation and clip the result in the interval [-1. randn(d0, d1, …, dn) : creates an array of specified shape and fills it with random values as per standard normal distribution. Adding noise. Input image data. It is always easiter to destroy (or critisize) than to build (or to create). Today we will be Applying Gaussian Smoothing to an image using Python from scratch and not using library like OpenCV. You can vote up the examples you like or vote down the ones you don't like. Here I used MATLAB function ‘randint’. From Google Maps and heightmaps to 3D Terrain - 3D Map Generator Terrain - Photoshop - Duration: 11:35. Brown Star → Where Adam Noise optimization method actually started to show signs of convergence. Aperture and simple PSF-fitting photometrymem¶. In this tutorial, you will discover how to implement the Bayesian Optimization algorithm for complex optimization problems. For example, if you wanted to create a signal with Additive White Gaussian Noise (AWGN), you could achieve this by using numpy’s random. we generally use a filter like the Gaussian Filter, which is a digital filtering technique that is often used to remove noise from an image. mode : str One of the following strings, selecting the type of noise to add: 'gauss' Gaussian-distributed additive noise. For more sophisticated modeling, the Minimizer class can be used to gain a bit more control, especially when using complicated constraints or comparing results from related fits. # For 50% of all images, we sample the noise once per pixel. Python OpenCV package provides ways for image smoothing also called blurring. This can be for testing or to add random data into an image. pyplot as plt import imageio numpy. jpg") Now apply the contrast. ndarray (with float dtype) or None, optional PSF kernel array to use for the fine structure image if fsmode == 'convolve'. distance_matrix (numpy. Python was created out of the slime and mud left after the great flood. Create a Python environment for PlantCV that includes the Python dependencies. gaussian noise added over image: noise is spread throughout; gaussian noise multiplied then added over image: noise increases with image value; image folded over and gaussian noise multipled and added to it: peak noise affects mid values, white and black receiving little noise in every case i blend in 0. The sharp change is edge. From your code I can see where my faults are. Algorithms The mean and variance parameters for 'gaussian' , 'localvar' , and 'speckle' noise types are always specified as if the image were of class double in the range [0, 1]. We propose here to use the mode of pixel values. Practical coverage of every image processing task with popular Python libraries Includes topics such as pseudo-coloring, noise smoothing, computing image descriptors. Gaussian noise are values generated from the normal distribution. First convert the RGB image into grayscale image. Here we show a standalone example of using PyStan to estimate the parameters of a straight line model in data with Gaussian noise. We demonstrated how we build a neural net using Python NumPy in 9 steps in Part 1 of this series, but it might be way too difficult for beginners to understand. In the image above, , I've saved some data in a numpy array. normal¶ numpy. jpg") Now apply the contrast. This is well illustrated by this simulation of a zombie outbreak in France (inspired by this blog post by Max Berggren). py --image /magepath/image. This is the type we're going to work on with OpenCV in this chapter!. The following are code examples for showing how to use cv2. However, how do I add Poisson noise in order to obtain the same SNR? I have tested imnoise with MATLAB, but with a certain constant chosen, the SNR changes for image for. But it still simply mixes the noise into the result and smooths indiscriminately across edges. The Gaussian filter applies a convolution with a Gaussian function to blur the image. gaussian_filter taken from open source projects. More On Adding Noise in An Image¶ "Any fool can throw a stong down a well, but it takes a wise man to git it out" It is always easiter to destroy(or critisize) than to build (or to create). This way you can avoid the clutter of bitmap files generated by PIL and left behind in your \Local Settings\Temp folder. Does anybody have a recipe for adding noise to a raster using python (possibly with GDAL/Numpy/PIL/or something else). Apart from Adaptive Gaussian threshold, there is also an Adaptive Mean threshold but it's not as good as Adaptive Gaussian threshold to remove the noise in an image. In earlier chapters, we have seen many image smoothing techniques like Gaussian Blurring, Median Blurring etc and they were good to some extent in removing small quantities of noise. Feature agglomeration vs. In this tutorial, you will discover how to implement the Bayesian Optimization algorithm for complex optimization problems. Finds Intensity Gradient of the Image. Let’s first blur and apply the inverse filter on the noiseless blurred image. OpenCV tutorial to detect and identify objects using Python in OpenCV. The noise comes from the normal distribution N(L,S). I'm already converting the original image into a grey scale to test some morphological methods to denoise (using PyMorph) but I have no idea how to add noise to it. Then we store the image in a numpy array. Firstly, the image is converted into grayscale so the opencv can process it easily and then a Gaussian blur is applied to the gray scale image so as to reduce the noise. - Added python_list_to_array() - Added min_barrier_distance() Non-Backwards Compatible Changes: Bug fixes: - Fixed numpy_image and pybind11 crashing python sometimes when certain types of conversions are attempted. Once completed and there is an array of processed data, use NumPy to take the mean of this processed data stack. They are extracted from open source Python projects. of Channels & Type of Image OpenCV C++. python,recursion. Sometimes we want to add noise into an image. This page documents the python API for working with these dlib tools. Finds Intensity Gradient of the Image. Typically, the form of the objective. Intermission: NumPy, Matplotlib, and SciPy¶ These three packages are the workhorses of scientific Python. Matplotlib is a library for making 2D plots of arrays in Python. If a time series is white noise, it is a sequence of random numbers and cannot be predicted. kaiser(101,b) pylab. When read with cv2. In OpenCV, image smoothing (also called blurring) could be done in many ways. You could also generate the linear SNR from your SNR in decibels, I've used this function in one of my projects once:. NumPy Array Object Exercises, Practice and Solution: Write a NumPy program to generate a generic 2D Gaussian-like array. Python Image Processing With OpenCV There are many image processing packages for Python. So we get different thresholds for different regions of the same image and it gives us better results for images with varying illumination. In this tutorial, we shall learn using the Gaussian filter for image smoothing. To get started, let's consider the simple example of one-dimensional non-linear regression on data corrupted by Gaussian noise. DLLs directory. Then generate random values for the size of the matrix. import numpy as np. The objective of the next two steps is to remove some edges to only keep those which are the most relevant. In those techniques, we took a small neighbourhood around a pixel and did some operations like gaussian weighted average, median of the values etc to replace the. Frequency response of the output image. PGURE-SVT includes two methods for integrating the algorithm into your Python workflow. Add some human noise (typos, things in the wrong boxes etc. نویز گاوسی چیه؟ ایجاد نویز گوسی و افزودن آن به تصویر در Python: الان که تعریف نویز و نویز گاوسی رو می‌دونیم برنامه نویسی بخش ساده‌ی کارمونه. Hence, when you do convolution with a constant input, you should expect 0 at output and not the same constant value (double derivative of constant is 0). 'poisson' Poisson-distributed noise generated from the data. Gaussian noise are values generated from the normal distribution. Join us in building a kind, collaborative learning community via our updated Code of Conduct. gaussian_filter takes an image and the standard deviation of the filter (in pixel units) and returns the filtered image. This post describes how to make (almost) any Instagram filter with about 15 lines of Python, using the (now-defunct) Gotham Instagram filter as a case study. Numpy+Vanilla is a minimal distribution, which does not include any optimized BLAS libray or C runtime DLLs. I wanted to point out some of the python capabilities that I have found useful in my particular application, which is to calculate the power spectrum of an image (for later se. It is always easiter to destroy (or critisize) than to build (or to create). Using Numpy. Should be equal to the S in the shape of the numpy arrays as for instance documented in scatter or plot_mesh. By voting up you can indicate which examples are most useful and appropriate. (Note that unsharp filtering may produce an equivalent result since it can be defined by adding the negative Laplacian image (or any suitable edge image) onto the original. This article will go into a bit of the background of FSK and demonstrate writing a simulator in Python. Once you have conda and git or GitHub Desktop installed, clone the PlantCV repository, open a command-line terminal application (on Windows there are other options but for this tutorial we will use the Anaconda Prompt application). imread("pyimg. I am trying to generate a complex Gaussian white noise, with zero mean and the covariance matrix of them is going to be a specific matrix which is assumed to be given. 8 , which does not produce any visible change to the image but helps remove artifacts. Let’s see how well we can find Nemo in an image. 04 alongside Windows 10 (dual boot) How to create a cool cartoon effect with OpenCV and Python How to create a beautiful pencil sketch effect with OpenCV and Python 12 advanced Git commands I wish my co-workers would know How to classify iris species using logistic regression. This approach offers a template for displaying multidimensional computed or experimental data as an image created with Python. But usually one would use numpy-based images and then it's simply adding some random-samples based on some distribution. There is no standard way. Firstly the data are generated by adding a gaussian noise to a linear function. (A) The original signal we want to isolate. This article will go into a bit of the background of FSK and demonstrate writing a simulator in Python. Eventually, we will cover how to write your own packages to better organize your own code or share your work, but this tutorial will focus on introducing some. numpy is included in PsychoPy2, and activated by using an import statement. So always better stick to OpenCV functions. by Kardi Teknomo. In the first case, global thresholding with a value of 127 is applied. This is the type we're going to work on with OpenCV in this chapter!. You’ll touch on all of the above and wrap up with a high-level comparison. An illustration of the log-marginal-likelihood (LML) landscape shows that there exist two local maxima of LML. This post is an additional note to official OpenCV tutorial : Smoothing Images ( Its corresponding Python code can be found here : smoothing. Whenever one slices off a column from a NumPy array, NumPy stops worrying whether it is a vertical or horizontal vector. Here is the algorithm: Blending the following input images A, B with mask image M. ContrastNormalization ((0. " wiki - Gaussian_noise. (the arrays can also use other types like floats and doubles, but for our image manipulation we mainly need to worry about the integer types). Attention! use noise-effect images for this technique. Reading Image Data in Python. > > To accomplish the described task, I have the following plan. A NumPy rewrite of JD Marble's 2D Improved Perlin Noise Python snippet. import matplotlib. Note that it should be three dimensional array even if it is a gray image data. I wanted to point out some of the python capabilities that I have found useful in my particular application, which is to calculate the power spectrum of an image (for later se. 5 can be downloaded via the anaconda package manager. output numpy. The following are code examples for showing how to use cv2. However this is not the case in median filtering, since the central element is always replaced by some pixel value in the image. This method balances processing time and output quality fairly well. (A) The original signal we want to isolate. One interesting thing to note is that, in the Gaussian and box filters, the filtered value for the central element can be a value which may not exist in the original image. We add a gaussian noise and remove it using gaussian filter and wiener filter using Matlab. augmenters as iaa ia. Images are added as per the equation below:. Cross-Platform C++, Python and Java interfaces support Linux, MacOS, Windows, iOS, and Android. The image is 2D pixels, the PSF fitting routine would do something like this. This is often convenient for importing proprietary file formats, for any pre- or post-processing of the data, and for plotting results. Parameters-----image : ndarray: Input image data. @returns: an pv. The right-most icon pops up a window which allows you to specify an output file for the plot. Now, NumPy supports various vectorization capabilities, which we can use to speed up things quite a bit. Here we will learn to apply the following function on an image using Python OpenCV: Bitwise Operations and Masking, Convolution & Blurring, Sharpening - Reversing the image blurs, Thresholding (Binarization), Dilation, Erosion, Opening/Closing, Edge detection and Image gradients,. I want to test the code with a given signal to noise ratios (SNR). This would work especially for noise that isn't just white noise, for example a bunch of sine waves with random frequencies, phase s. An introduction to smoothing¶ Smoothing is a process by which data points are averaged with their neighbors in a series, such as a time series, or image. medianBlur and cv2. Once you have created an image filtering function, it is relatively straightforward to construct hybrid images. Join us in building a kind, collaborative learning community via our updated Code of Conduct. , using a Gaussian filter) before applying the Laplacian. To generate a vector with 10 000 numbers following a gaussian distribution of parameters mu and sigma use. 著者: Emmanuelle Gouillart, Gaël Varoquaux. Or, how to add noise to an image using Python with OpenCV?. This article will go into a bit of the background of FSK and demonstrate writing a simulator in Python. MatPlotLib Tutorial. I ended up treating the spectrogram as an image and using the image processing toolkit and techniques from scipy to find peaks. Here I used MATLAB function ‘randint’. useage: python cannycode. Here is the algorithm: Blending the following input images A, B with mask image M. Numpy と Scipy を利用した画像の操作と処理¶. This is what we are going to do in this section. A 2d Gaussian fit is done on each of the maxima constraining the position on the subimage and the sigma of the fit. seed (50) # Covariance matrix def covMat (x1, x2, covFunc, noise = 0): cov = covFunc (scipy. The noise comes from the normal distribution N(L,S). Today we will be Applying Gaussian Smoothing to an image using Python from scratch and not using library like OpenCV. your function should take an clean image and a parameter say sigma and it should return a noisy image. Copy an image to folder project. Gaussian Blur In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function. As for the gif, I will release it soon (implemented with. The standard random module implements a random number generator. The next code block performs the above steps. Parameters-----image : ndarray: Input image data. Signal-to-Noise in MRI FFT of Gaussian Noise • Note sqrt(N) scaling preserves noise energy 3. However this is not the case in median filtering, since the central element is always replaced by some pixel value in the image. The leftmost plot shows the generated image, the center shows a 3D render of the image, taking intensity values as height of a 3D surface, and the right one shows the shape index (s). Input image data. They are extracted from open source Python projects. The Numpy Stack in Python - Lecture 23: Sampling Gaussian 1 Python Tutorial for Beginners [Full Course] How to insert images into word document table - Duration:. shape to get the dimensions of the image. Laplacian is a kernel used for calculating the edges in an image. One interesting thing to note is that, in the Gaussian and box filters, the filtered value for the central element can be a value which may not exist in the original image. 's&p' Replaces random pixels with 0 or 1. We use cookies for various purposes including analytics. util import random_noise im = random_noise(im, var=0. Or, how to add noise to an image using Python with OpenCV?. The sharp change is edge. , noise_sigma, input. ) to the image in Python with OpenCV This question already has an answer here: Impulse, gaussian and salt and pepper noise with OpenCV 4 answers I am wondering if there exists some functions in Python with OpenCV or any other python image processing library that adds Gaussian or salt an. Adding noise to the original image. So the main contribution of that paper is rather using normal gradient descent, we are going to add a Gaussian Noise to every gradient with Mean Value of 0 and certain Standard Deviation Value. To get started, let's consider the simple example of one-dimensional non-linear regression on data corrupted by Gaussian noise. Applying a low-pass blurring filter smooths edges and removes noise from an image. ndarray Blurred data. , 20% of noise) Try two different denoising methods for denoising the image: gaussian filtering and median filtering. Image noise is a random variation in the intensity values. In this OpenCV with Python tutorial, we're going to be covering how to try to eliminate noise from our filters, like simple thresholds or even a specific color filter like we had before: As you can see, we have a lot of black dots where we'd prefer red, and a lot of other colored dots scattered. njit function within which I am trying to put an integer within a string array. layers import Conv2D, MaxPooling2D from keras import backend as K import numpy as np import pescador batch_size = 128 num_classes = 10 epochs = 12. spatial import matplotlib. uneven illumination). That being said, this really isn't going to be a primer on Perlin Noise itself, rather it's going to focus on its implementation in Python. Simple Python programs process a given number of images, recorded consecutively from the same subject. 04 alongside Windows 10 (dual boot) How to create a cool cartoon effect with OpenCV and Python How to create a beautiful pencil sketch effect with OpenCV and Python 12 advanced Git commands I wish my co-workers would know How to classify iris species using logistic regression. PRNG options include the random module from Python’s standard library and its array-based NumPy counterpart, numpy. OpenCV is a highly optimized library with focus on real-time applications. Firstly the data are generated by adding a gaussian noise to a linear function. Adding noise. imread(), so it doesn't matter which OpenCV or Pillow is used, but be aware that the color order is different. The encoding process repeats the following: multiply the current total by 17 add a value (a = 1, b = 2, , z = 26) for the next letter to the total So at. array_gaussian_noise=mu+uint8(abs(floor(randn(size_1,size_2)*sigma))) The first one would simply remove all negative noise, the second one, brings to positive all negative noise values. normal(loc = 0. Since derivative filters are very sensitive to noise, it is common to smooth the image (e. To get the image shape or size, use ndarray. OpenCV 3 image and video processing with Python OpenCV 3 with Python Image - OpenCV BGR : Matplotlib RGB Basic image operations - pixel access iPython - Signal Processing with NumPy Signal Processing with NumPy I - FFT and DFT for sine, square waves, unitpulse, and random signal Signal Processing with NumPy II - Image Fourier Transform : FFT & DFT. These examples assume you are using the IPython pylab mode which automatically imports a number of numerical and plotting routines into the session. Grauman Smoothing with larger standard deviations suppresses noise, but also blurs the image Reducing Gaussian noise. Practical coverage of every image processing task with popular Python libraries Includes topics such as pseudo-coloring, noise smoothing, computing image descriptors. However, I am not planning on putting anything into production. We can achieve this by adding random Gaussian distribution noise and multiplying it by some constant value. pyplot as plt from numpy import loadtxt import numpy as np from pylab add some noise to the test images. Gaussian filters have the properties of having no overshoot to a step function input while minimizing the rise and fall time. Algorithms The mean and variance parameters for 'gaussian' , 'localvar' , and 'speckle' noise types are always specified as if the image were of class double in the range [0, 1].