Matlab imresize bicubic. Start by reading and displaying an image.

Matlab imresize bicubic The different methods supported how does matlab implement the command: imresize(<image>,<scaling factor>,'bicubic'); imresize offers 'bilinear' and 'bicubic' methods for resizing images. Matlab imresize function. Learn more about imresize, bicubic, resizecolumnscore, interpolation . Thus their outputs are The imresize function offers many built-in kernels that perform bilinear, bicubic, and Lanczos resampling. imresize(old_image, 0. how does this operation work? By default, imresize uses bicubic interpolation. 5 in Matlab, it's contrast to my experience. fromarray(arr). In fact, the proposed implementation of python's imresize had the main goal not to add N+1 version of image resize (scipy. ; Build 10 bits YUV420 sample file from the 8 bits sample (singe frame for testing): imresize is blurring my image!. example [Y,newmap] = By default, imresize uses bicubic interpolation, but you can specify other interpolation methods or interpolation kernels. Show -2 older comments Hide -2 older comments. Hi, I am wondering how work Matlab function imresize with bicubic interpolation. B = imresize(A,m,method) returns an image that is m times the size of A. With interp2 you cannot specify a simple multiplication factor that you want to scale your image by the way you can with imresize. e. However, because this is as an exercise to test an understanding of MATLAB with techniques learned so far without using other By default, imresize uses bicubic interpolation. 9. and i need to get to the same results like matlab. 99999, interp I would start on Wikipedia. For upsampling it is clear that these are interpolation methods that use 2x2 or 4x4 neighborhoods to est Hi, I am wondering how work Matlab function imresize with bicubic interpolation. py at master · sanghyun-son/bicubic_pytorch imresize using bicubic interpolation. Following is a small example on how to do this: I see the imresize function, which has an option for 'method'. If you look at the source code of the Matlab implementation there is a chance you will learn a copyrighted method, which would preclude you from implementing it By default, imresize uses bicubic interpolation. Python Version how does matlab implement the command: imresize(<image>,<scaling factor>,'bicubic'); the other types of interpolations are easy to understand and implement. Hi, I am downsampling my satellite images (. Anti-Aliasing Algorithm for Pixelart-2. MATLAB, a widely used platform for numerical computing and data analysis, provides powerful tools for image manipulation, including resizing. You can also define a custom kernel and then resize images using the custom By default, the imresize function uses the bicubic interpolation algorithm. B = imresize(A,[numrows numcols]) returns image B that has the number of rows and columns specified by the two-element Learn more about imresize, downsample, bicubic Image Processing Toolbox. However, current Numpy and PyTorch implementations don't have the function of anti-aliasing. example [Y,newmap] = By default, imresize uses bicubic interpolation. The goal of this repository is to provide a MATLAB-like bicubic interpolation in a widely-used By default, imresize uses bicubic interpolation. imresize and I am using Matlab's imresize function to downscale a 3000x2000 image to 120x80 pixel using bicubic interpolation. I have implemented a code for image warping using bilinear interpolation: Matlab image rotation I would like to improve the code by using bicubic interpolation to rotate the image WITHOUT using Learn more about imresize, downsample, bicubic Image Processing Toolbox. B = imresize(A,[mrows ncols],method) returns an image of size Learn more about dlarray, imresize, deeplearning Image Processing Toolbox I want to perform bicubic interpolation on 'dlarray' type objects. Learn more about imresize, bicubic interpolation, , I am doing a project on computer graphics and have been asked to implement the matlab's imresize function in C++, using bicubic interpolation. This example use nearest neighbor interpolation. What does imresizemex do in Matlab imresize function? 0. Behavioral Reference. For upsampling it is clear that these are interpolation methods that I tried to implement the algorithm in figure 3 of this paper using Matlab. If m is between 0 and 1. This example shows how to resize an image using the imresize function. As you know, if the scale factor is less tha Skip to content. I was interested myself in finding out why there's a difference. , PIL, OpenCV, PyTorch, ) are not consistent with the MATLAB, especially for a bicubic kernel. 0, B is smaller than A. pic_new = imresize( pic, newSize, 'bicubic' ); Where newSize is the new size of the image (height and width). The exact code line that is no longer working is this: new_image = scipy. If n is 0 (zero), imresize omits the Reading 10 bit YUV420: Assumptions: Each 10 bits component is stored in 2 bytes (no "bits packing"). If you'd like to compare apples J = imresize(I, 2, 'bicubic');%in your case. imresize, skimage. I am attempting to implement two dimensional bicubic interpolation algorithm in Matlab. Search imresize uses interpolation to determine the values of these pixels, imresize bases the weightings on the distance each pixel is from the point. 75, and Learn more about imresize, bicubic, resizecolumnscore, interpolation . By the way, in that comment, the author states that alpha = -0. Code is given below. interp2 does 2D interpolation and instead of a scale input you need to provide it with the x-y coordinates of the points between the pixels that you want to interpolate. imresize bicubic. The following script down samples HR images to LR images for Super-Resolution data preparation. The problem is, there are only 3 options: nearest, bilinear, bicubic. 5 vs a=-0. You can choose the nearest neighbor, bilinear, or Lanczos-2 interpolation algorithms by setting the 'Method' name-value argument to 'nearest', Run the command Hello, I am doing a project on computer graphics and have been asked to implement the matlab's imresize function in C++, using bicubic interpolation. I: input image. I am using functions like 'dlconv' and 'batchnorm' that return/accept 'dlarray' objects, so I have to do the resizing on 'dlarray' Learn more about imresize, downsample, bicubic Image Processing Toolbox. Yes, to downsample your satellite images from 2m to 10m resolution using the `imresize` function in MATLAB, Using imresize it can be easily achieved. 'bicubic' uses bicubic interpolation. Sign In; 此 MATLAB 函数返回图像 B，它是将 A 的长宽大小缩放图像 scale 倍之后的图像。 By default, imresize uses bicubic interpolation. 1. You could use the 'imresize' function instead of 'dlresize'. example [Y,newmap] = Learn more about imresize, downsample, bicubic Image Processing Toolbox. For upsampling it is clear that these are interpolation methods that use 2x2 or 4x4 neighborhoods to est From Matlab's doc: 'bicubic' Bicubic interpolation (the default); the output pixel value is a weighted average of pixels in the nearest 4-by-4 neighborhood. ; Storage format is the same non-standard interlace format as the uint8 sample. example [Y,newmap] = how does matlab implement the command: imresize(<image>,<scaling factor>,'bicubic'); the other types of interpolations are easy to understand and implement. but in case of bicubic, when the scal Aquí nos gustaría mostrarte una descripción, pero el sitio web que estás mirando no lo permite. I would like to decrease the resolution of my images from 2m to 10m. For example, shrinking an image by 1/2 along the rows and leaving number of columns Image resizing is one of the essential operations in computer vision and image processing. Write // Bicubic, Zoom, Anti As discussed in my previous question imresize - trying to understand the bicubic interpolation I have recompiled openCV with -0. MATLAB Learn more about image processing, imresize, downscaling, bicubic interpolation . imresize uses bicubic interpolation by default, so its results will be slightly different. For upsampling it is clear that these are interpolation methods that By default, imresize uses bicubic interpolation. So it can be plug in nerual networks . I have successfully implemented a grayscale version (real double type) of imresize with bicubic How does the function "imresize" work Learn more about resolution, enhancement, improvement, image, image processing, imresize, resolution increasing During my internship I discovered the function "imresize" which I used it to enhance the resolution of images (for example : I transformed a 32x32 image into a 128x128 image) and it gave me really By default, imresize uses bicubic interpolation, but you can specify other interpolation methods or interpolation kernels. For each pixel in the output image, imresize is doing a point transformation to find where the corresponding point maps in the input image. They outputs different results with the results on matlab version. MATLAB Answers. Resize scale factor, specified as a positive number or 3-element vector of positive numbers. See Wiki for more information. example [Y,newmap] = Need Explanation of Bicubic Interpolation, in Learn more about image processing, image interpolation Image Processing Toolbox Anti-Aliasing Filter for matlab imresize. Learn more about imresize, bicubic interpolation, anti aliasing how does matlab implement the command: imresize(<image>,<scaling factor>,'bicubic'); the other types of interpolations are easy to understand and implement. If you look at the source code of the Matlab implementation there is a chance you will learn a copyrighted method, which would preclude you from implementing it Recently, I was talking with MathWorks writer Jessica Bernier about the reference page for the imresize function. Once imresize has formed a collection of remapped points, interpolatation is performed to resolve sub-pixel remapped locations (the default of imresize is bicubic interpolation). You can choose the nearest neighbor, bilinear, or Lanczos-2 interpolation algorithms by setting the 'Method' name-value A version of matlab function 'imresize' using 'bicubic' interpolation, realized by pytorch and could acclearte by cuda. For upsampling it is clear that these are interpolation methods that use 2x2 or 4x4 neighborhoods to establish a For obtaining the low res images we use the Matlab function "imresize" with default settings (bicubic interpolation) and the desired downscaling factors: 2, 3, and 4. imresize and torch. In today's post, I'll compare the supported interpolation kernels on a sample image, and then I'll show you how to use your own kernel. If you omit the method argument, imresize uses the default method of 'nearest'. For upsampling it is clear that these are interpolation methods that use 2x2 or 4x4 neighborhoods to est I would start on Wikipedia. Thanks, this is nearly a solution but it's not as mathematically sound as I'd like; since the scaling is 1:4, the new pixel centres are equally distant from the four old pixel centres, and MATLAB seems to arbitrarily select one pixel (the upper-right) of the four. Learn more about imresize, bicubic interpolation, image processing . You can choose the nearest neighbor, bilinear, or Lanczos-2 interpolation algorithms by setting the 'Method' name-value argument to 'nearest', Run the command By default, imresize uses bicubic interpolation. By default, the imresize function uses the bicubic interpolation algorithm. I want the theorotical explanation of the imresize function for downscaling the image. These are my findings (as I understood the algorithms, please correct me if I make any mistakes). n is an integer scalar specifying the size of the filter, which is n-by-n. How matlab bicubic imresize do? anti-alising; compare with opencv bicubic imresize; implementation in codes/data/util As a comparison, in Matlab this doesn't occur (I am aware of a slight difference in weighting schemes as appears here: imresize comparison - Matlab/openCV). Hi, I am doing a project on computer graphics and have been asked to implement the matlab's imresize function in C++, using bicubic interpolation. Dear MATLAB users, imresize offers 'bilinear' and 'bicubic' methods for resizing images. If you look at the source code of the Matlab implementation there is a chance you will learn a copyrighted method, which would preclude you from implementing it elsewhere. example [Y,newmap] = imresize(X,map, there can be a small numerical mismatch between the results in MATLAB ® and the generated This example shows how to resize an image using the imresize function. The test input matrix: input B = imresize(A,scale) 缩放图像A 至scale倍。The input image A can be a grayscale, RGB, or binary image. Did anyone implemented the parametric Mitchell-Netravali kernel [1] that is used as default in ImageMagick and is willing to share the Matlab code? Thank you very much! If you look at the documentation for previous versions of MATLAB, under the Extended Capabilities section for gpuArray in the imresize doc, there is a note that only bicubic interpolation was supported for gpuArray/imresize in R2020b and previous versions: imresize using bicubic interpolation. example [Y,newmap] = imresize(X,map, there can be a small numerical mismatch between the results in MATLAB ® and the generated Track 1: bicubic uses the bicubic downscaling (Matlab imresize), one of the most common settings from the recent single-image super-resolution literature. By default, imresize uses bicubic interpolation. While MATLAB's imresize function is used as a standard, implementations from other libraries (e. example. You do not have any more information in the output image than you started with in the input image, you have simply interpolated to create a larger grid than you started with. Gr = imresize(Gr, 0,5); I understand your point. example [Y,newmap] = By default, imresize uses bicubic interpolation by default. For upsampling it is clear that these are interpolation methods that use 2x2 or 4x4 neighborhoods to est imresize using bicubic interpolation. This function is defined in the Helper Functions section at the end of this example. Jessica pointed out that we don't have an example I would start on Wikipedia. See this I found this topic imresize - trying to understand the bicubic interpolation could solve your confusion, especially for the comment with 7 upvotes. elif method == 'bilinear': kernel = triangle. B = imresize(A,outputSize) 指定图像大小缩放。 Contribute to xinntao/matlab_functions_verification development by creating an account on GitHub. What is intriguing to me is simply the 'geometric transformation' that will enable accessing (x0, y0), etc. I had a doubt in the resizing of an image using bicubic interpolation In matlab, at a stage, they have used a function resizeColumnsCore(double(in), weights', indices'); in this, the m Skip to content. The new aspect ratio can be arbitrary and does not have to be the same as the aspect ratio of the new image. so for an example I want to get just the first pixel of my image If you actually want to match MATLAB's output, you need to disable anti-aliasing. I had a doubt in the resizing of an image using bicubic interpolation In matlab, at a stage, they have used a function resizeColumnsCore(double(in), weights', indices'); in this, the m Skip to By default, imresize uses bicubic interpolation. I would start on Wikipedia. Search Learn more about imresize, downsample, bicubic Image Processing Toolbox. Search Answers Answers. 75f. After reading the imresize. I am looking at some code that produces the necessary outputs and it uses imresize(A,n) where A is the complex matrix and n is the resize factor. Upsample(interpolation) and so on. Skip to content. Scale Diff (Ours) Diff ratio (Ours) Diff (bicubic_pytorch) Diff ratio (bicubic_pytorch) Downsample X2: 2: 0. From Matlab imresize. - bicubic_pytorch/core. You can extract data from your 'dlarray' object using the 'extractdata' function and then pass it to 'imresize'. To evaluate and compare interpolation By default, imresize uses bicubic interpolation, but you can specify other interpolation methods or interpolation kernels. 5]. function. 00%: 4: 0. Learn more about downsampling, imresize, bicubic . In this you can specify several details like interpolation method and filter kernel. example [Y,newmap] = Image resizing is one of the essential operations in computer vision and image processing. example [Y,newmap] = Contribute to xinntao/matlab_functions_verification development by creating an account on GitHub. m source, you imresize uses interpolation to determine the values of these pixels, imresize bases the weightings on the distance each pixel is from the point. Learn more about imresize . * Imresize uses inverse mapping to figure out where each point in the output grid maps in the input grid. For a fair comparison I have seen that there was an interest in custom interpolation kernels for resize (MATLAB imresize with a custom interpolation kernel). I stepped through the impementation of Matlab and noticed that a huge number of kernel weights are computed for each output pixel, not just 4x4 as I expected. Then, display the bilinear interpolation kernel for a neighborhood of [-3. for imresize. So the only explanation for this is that they use different weighting strategy to get the average value. By default, imresize uses bicubic interpolation, but you can specify other interpolation methods or interpolation kernels. the imresize with default settings) just to provide engineers and scientists working on Super Resolution the i'm trying to implement bicubic interpolation; this is a follow-up question to my question:MATLAB vs C++ vs OpenCV - imresize about imresize, so i know openCV doesn't do cubic interpolation like matlab. example [Y,newmap] = imresize(X,map, there can be a small numerical mismatch between the results in MATLAB ® and the generated Anti-Aliasing Filter for matlab imresize. I wrote 2 functions to test, and I figured out Matlab set alpha = -0. png format) with Imresize bicubic function. I had a doubt in the resizing of an image using bicubic interpolation In matlab, at a stage, they have used a function resizeColumnsCore(double(in), weights', indices'); in this, the m By default, the imresize function uses the bicubic interpolation algorithm. If scale is from 0 through 1. J: Resized image. You can also define a custom kernel and then resize images using the custom imresize takes different inputs from interp2. I understand how it works in the middle of image where it have full access to all data, then usage of bicubic interpolation is quite straight forward. Search A collection of different MATLAB scripts and tools - mindThomas/MATLAB-tools Hello, I am doing a project on computer graphics and have been asked to implement the matlab's imresize function in C++, using bicubic interpolation. If this is not the case the default value ,which is bicubic, is applied. 4 Comments. While many interpolation methods in python like scipy. The goal of this repository is to provide a MATLAB-like bicubic interpolation in a widely-used how can I use my function as an interpolation method for imresize function in MATLAB? I read MATLAB's help about the way to use a custom function for interpolation method, but there was not The imresize command will by default use the bicubic method. For upsampling it is clear that these are interpolation methods that use 2x2 or 4x4 neighborhoods to est B = imresize(,method,n) When the specified output size is smaller than the size of the input image, and method is 'bilinear' or 'bicubic', imresize applies a lowpass filter before interpolation to reduce aliasing. 0. There you can see, that matlab is not using a 2x2 neibourhood when using the By default, imresize uses bicubic interpolation. how does this operation work? Anti-Aliasing Filter for matlab imresize. I want to use an old script which still uses scipy. More info: For obtaining the low res images we use the Matlab function "imresize" with default settings (bicubic interpolation) and the desired downscaling factors: 2, 3, and 4. 5: scaling factor 0 Comments. If scale is greater than 1. m (edit imresize) and take a look at the contributions-function. Applying a scale geometric transformation to an image is not a "resolution enhancement" technique. but in case of bicubic, when the scaling factor is less than 1, it does the anti-aliasing filter operation. Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting! Based on the matlab doc bicubic is the default value for this function. Anti-Aliasing Filter for matlab imresize. Show 2 older comments Hide 2 older comments. INTER_CUBIC - a bicubic interpolation over 4x4 pixel neighborhood. resize, numpy. Learn more about imresize, downsample, bicubic Image Processing Toolbox. As you know, if the scale factor is less tha Vai al contenuto. A version of matlab function 'imresize' using 'bicubic' interpolation, realized by pytorch and could acclearte by cuda. Th Looking at imresize in MATLAB, here are the weights functions for the linear and cubic kernels: % or simply: 1-abs(x) for x in [-1,1] f = (1+x) . B = imresize(A,[numrows numcols]) returns image B that has the number of rows and columns specified by the two-element vector [numrows The bilinear method uses a triangular interpolation kernel, which is defined as: Create a bilinear interpolation kernel using a function called triangleResampling. Navigation Menu Toggle navigation. Sign in to comment. Anything that you can learn there is very unlikely to be copyrighted by anyone. bicubic-interpolation-pytorch-version-the-same-results-with-matlab-imresize has no bugs, it has no vulnerabilities and it has low support. * ((-1 <= x) & (x < 0)) + (1-x) . 5, 3. example [Y,newmap] = imresize(X,map, there can be a small numerical mismatch between the results in MATLAB ® and the generated The imresize function offers many built-in kernels that perform bilinear, bicubic, and Lanczos resampling. Accuracy. Sign in Product if method == 'bicubic': kernel = cubic. And from OpenCV's doc:. Possible methods are Learn more about imresize, downsample, bicubic Image Processing Toolbox. 5f instead of -0. array(Image. 01%: By default, imresize uses bicubic interpolation, but you can specify other interpolation methods or interpolation kernels. zoom, PIL resize etc), but to do very similar to MatLab's bicubic imresize (i. example [Y,newmap] = I didn't want to use 'interp2' or any other short-cut. , at the edges of an image, without generating errors (even if it requires padding that image, first). It does not show up in the help for my MATLAB. To evaluate and compare interpolation The imresize function offers many built-in kernels that perform bilinear, bicubic, and Lanczos resampling. Sign in Product GitHub Copilot. Start by reading and displaying an image. transform. There is an excellent builtin matlab function for this: imresize. however I still get different results although the input is the same, I guess i'm using resize() function wrong can you please help? the matlab code is just. Instead the devs recommend to use either numpy. As you know, if the scale factor is less than one, we need a anti-aliasing filter while interpolation. For upsampling it is clear that these are interpolation methods that imresize in MATLAB uses bicubic interpolation by default and I know for a fact that MATLAB uses custom kernels to do so, and so it will be much more difficult to match their outputs if you use bicubic interpolation between the methods. For upsampling it is clear that these are interpolation methods that resize functions with 'bicubic' as option in python and matlab are different and published papers recently generally use matlab to produce low-resolution image; Implement SRCNN via Keras with Theano as backend. Probably, they check if the passed value is one of the predefined values. nn. I had a doubt in the resizing of an image using bicubic interpolation In matlab, at a stage, they have used a function resizeColumnsCore(double(in), weights', indices'); in this, the m By default, imresize uses bicubic interpolation. If you specify a scalar, then imresize3 applies the same scale factor to each dimension in the volume. Just hit F1 while imresize is selected in the matlab gui. g. If you specify a 3-element vector, then By default, the imresize function uses the bicubic interpolation algorithm. By default, imresize uses bicubic interpolation, but you can specify other interpolation bicubic-interpolation-pytorch-version-the-same-results-with-matlab-imresize is a Python library typically used in Artificial Intelligence, Machine Learning, Deep Learning, Pytorch, Numpy applications. You can alternatively specify one of several other built-in interpolation imresize - trying to understand the bicubic interpolation. You can also specify your own custom interpolation kernel. You can choose the nearest neighbor, bilinear, or Lanczos-2 interpolation algorithms by setting the 'Method' name-value argument to 'nearest', Run the command Learn more about image processing, bicubic interpolation Image Processing Toolbox Is there any website that I can look at the source code of bicubic? I want to implement in Verilog but i have no idea how matlab done with bicubic the Need Explanation of Bicubic Interpolation, in Learn more about image processing, image interpolation Image Processing Toolbox. C implementation of MATLAB built-in function of imresize. B = IMRESIZE(A,M,'method') returns an image matrix that is M times larger (or smaller) than the image A. ) Share. Open the imresize. Bilinear and bicubic are averaging/mean methods, but is there any way to set the neighborhood size / weighting? The main problem is, I need to do it with a 'median' interpolation method, instead of mean. Recommend to use bicubic_pytorch. Search By default, imresize uses bicubic interpolation. - vujadeyoon/MATLAB2016b-imresize. By default, imresize uses bicubic interpolation. The image B is computed by interpolating using the method in the string 'method'. Here's a short Matlab code snippet that saves the smallest value in any of 1000 random downsized matrices (5,5)=1; imresize(I,[5 5],'bicubic') Learn more about imresize, downsample, bicubic Image Processing Toolbox. imresize() which is not only deprevated but removed entirely from scipy. If you look at the source code of the Matlab implementation there is a chance you will learn a copyrighted method, which would preclude you from implementing it Bicubic is an interpolating method for data points on a two-dimensional regular grid. Does anyone has an idea how Matlab is computing these kernel weights ? The documentation for the function seems to be incomplete. In this article, we’ll explore how to resize images in MATLAB using the built-in Anti-Aliasing Filter for matlab imresize. B = imresize(A,[numrows numcols]) returns image B that has the number of rows and columns specified by the two-element vector [numrows numcols]. resize(). By default, imresize uses bicubic interpolation, but you can specify other interpolation This is sort of a follow-up to your previous questions about the difference between imresize in MATLAB and cv::resize in OpenCV given a bicubic interpolation. 0, B is larger than A. MATLAB by default will perform anti-aliasing on the images to ensure the output looks visually pleasing. confusion regarding "imresize" in MATLAB? Hot Network Questions What is The imresize function offers many built-in kernels that perform bilinear, bicubic, and Lanczos resampling. It requires OpenCV and NumPy. If m is greater than 1. You can also define a custom kernel and then resize images using the custom kernel. I had a doubt in the resizing of an image using bicubic interpolation In matlab, at a stage, they have used a function resizeColumnsCore(double(in), weights', indices'); in this, the m 1. imresize using bicubic interpolation. . misc. Contribute to fatheral/matlab_imresize development by creating an account on GitHub. The input is a two dimensional array and the output is the interpolated result. We then interpolate within the input grid to determine the output grid By default, imresize uses bicubic interpolation, but you can specify other interpolation methods or interpolation kernels. %Decomposing %Bicubic interpolation by factor 2 on each subbands LL1 = imresize(LL,2,'bicubic'); LH1 = imresize(LH,2,'bicubic'); HL1 = Anti-Aliasing Filter for matlab imresize. Thank you for taking the time to share this, very useful (I'll be referring to it whenever I forget all these details)! Reading "interpolation of samples" section and the last part reminded me of a previous question where we looked at the bicubic interpolation and the implementation difference between MATLAB and OpenCV (in that case it was the constant a=-0. resize()) or skimage. 'imresize' has an option to use bicubic interpolation. Data is stored in lower part of each byte (each uint16 element holds a value in range [0, 1023]). example [Y,newmap] = imresize(X,map, there can be a small numerical mismatch between the results in MATLAB ® and the generated By default, imresize uses bicubic interpolation by default. For upsampling it is clear that these are interpolation methods that use 2x2 or 4x4 neighborhoods to est A PyTorch implementation of widely-used bicubic interpolation, which is fully compatible with MATLAB. m documentation, I don't understand what happens if the input image is actually a matrix of complex numbers. Toggle Main Navigation. hbdwpg gfefp iiub veuews qppgsa zjf gubow evjuc bhr atxa