The scipy.interpolate.interp2d() function performs the interpolation over a two-dimensional grid. Implementing Bicubic Interpolation with Python Importing the necessary modules: We import all dependencies like cv2 (OpenCV), NumPy, and math. In other words, the algorithm simply calculates the average value of the boxed pixels. Using the scipy.interpolate.interp2d() function to perform bilinear interpolation in Python. It is better to create a function for bilinear interpolation and resizing. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. A simplified version of linear interpolation works like the following: imagine we have a point \(C\) with an unknown value, as well as points (point \(A\) and point \(B . For example, suppose we want to shrink the image to its third in its width and height. cv2.INTER_LINEAR: This option is primarily used when zooming is required. Mathematica cannot find square roots of some matrices? This class returns a function whose call method uses spline interpolation to find the value of new points. However, the quality of the resulting image will be higher. rev2022.12.11.43106. When x is an integer, x_floor and x_ceil will have the same value as x. apply resize () to increase the dimensions of an image with nearest neighbour interpolation. {\textstyle F} Now we calculate the scaling factors along the two dimensions. 7. from . Here, I will walk you through the implementation of Bilinear Interpolation to resize images and well also discuss some problems that we might face on the way, and the solutions as well. Bilinear interpolation is performed using linear interpolation first in one direction, and then again in the other direction. We assume the pixels locate in the middle of pixel boxes, and boundaries have their own coordinates. Weve implemented Bilinear Interpolation to resize an Image. And I will explain it next. INTER_NEAREST a nearest-neighbor interpolation, INTER_LINEAR a bilinear interpolation (used by default). The set of weights can also be interpreted as a set of generalized barycentric coordinates for a rectangle. One solution is to clip the results to [0, 255]. This is done by multiplying the coordinate values i,j with the scaling factors of the corresponding dimensions to obtain x and y values. This process is repeated for each pixel forming the object being textured.[4]. If the interpolation is 'none', then no interpolation is performed for the Agg, ps and pdf backends. What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked. Ready to optimize your JavaScript with Rust? Not the answer you're looking for? 0 Input image (2 x 2 pixels): Code: resize(_inputImage, outImage, Size(256,256),INTER_NEAREST); imshow(_windowName, outImage); Expected result (256 x 256 pixels): Change image range using linear interpolation. cv2.resize (src, dsize [, dst [, fx [, fy [, interpolation]]]]) where Examples of using cv2.resize () function Resizing an image can be done in many ways. This also means that the interpolated value is a copy of the left pixel. alpha : This parameter is a intensity of the color. It may be a preferred method for image decimation, as it gives moire'-free results. You might be thinking, why should I waste time on thinking and writing a code to resize images when I can have an editing application or a robust library take care of it. In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. cv2.INTER_LINEAR - It uses bilinear interpolation, which is preferably used for scaling up the image to a larger size. We first do linear interpolation in the x-direction. Love podcasts or audiobooks? ] We proceed by interpolating in the y-direction to obtain the desired estimate: Note that we will arrive at the same result if the interpolation is done first along the y direction and then along the x direction. For a beginner like me, I wouldve thought that scaling a row like [0, 1] to 4 columns would be [0, 0.3, 0.6, 1]. This option uses inverse transformation technique for interpolation. This is illustrated in Figure 2 (Of course, the width of the image in the figure is not 9). For the Agg, ps and pdf backends, interpolation='none' works well when a big image is scaled down, while interpolation='nearest' works well when a small image is scaled up. Therefore, the first three indices of ofs are 0, 3, 6. Why would Henry want to close the breach? Bazel version (if compiling from source): GCC/Compiler version (if compiling from source): CUDA/cuDNN version: GPU model and memory: Exact command to reproduce: During the calculation of the two positions to interpolate between, say x1 or x2 in the bi-linear interpolation, python was returing 0 for simple division such as 1/2, and not 0.5, thus there weren't always two points to interpolate between resulting in the NN-type output. Plus this statement: This means, when inv_scale_x is an integer, fx is always 0, and the coefficients are always 1 and 0. X: This parameter is the data of the image. So xofs marks the starting boundaries of all such averaging blocks. Note that in the MATLAB code, x is the output image coordinate, u the input image coordinate and scale is the ratio of output image width over input image width, the same as inv_scale_x in OpenCV. And this includes answers in sites like StackOverflow. This is the default option in cv2.resize() cv2.INTER_NEAREST - It uses nearest-neighbor interpolation, which is fast but produces blocky images. It is the Bilinear interpolation method and it is the default interpolation function in OpenCV. Why does Python return 0 for simple division calculation? Bilinear interpolation is the default strategy. And the behaviour is also slightly different depending on whether the scale factor is an integer or not. INTER_AREA resampling using pixel area relation. It contains an if/else check to avoid division by 0 in case new_h or new_w is equal to 0. I am trying to 'enlarge' pixels - i.e. It turns out that most of the time when people mention those interpolation methods, they just rephrase the brief explanation above, or just directly copy it. There can be three possible cases: Case 1:When both x and y have integer values. interpolation: It gives us the option of different methods of resizing the image. Some of the possible interpolation in openCV are: INTER_NEAREST - a nearest-neighbor interpolation INTER_LINEAR - a bilinear interpolation (used by default) INTER_AREA - resampling using pixel area relation. It may be a preferred method for image decimation, as it gives moire-free results. chadrick-kwag.net/cv2-resize-interpolation-methods, https://github.com/crackaf/triple-recovery/tree/main/tests. Making statements based on opinion; back them up with references or personal experience. 69: 70 """ 71: img . Which kind of interpolation best for resizing image? In such a case, there is no need to estimate the pixel value. Resizing images is one of the technics in OpenCV. Then iscale_x = 3, and iscale_y = 3. As a result, both q1 and q2 will be 0 and finally, q will be 0 as well. How do I delete a file or folder in Python? To overcome such problem you should find out the new size of the given image where the interpolation can be made. which can be found in images.internal.resize.contributions. For non-integer shrinking, the idea is still the same, but weight will change depending on how much a pixel in the original image is included in a window (note that this time the window size has decimal values). Depending on how much we want to scale our original image, INTER_AREA may do different things. My command: resized = F.interpolate (rgb_image_tensor.type (torch.FloatTensor), (256,256),mode='bilinear') I show the image by using result = torchvision.transform.functional.to_pil_image (resized [0]) result.show () Default way works, shows the image is resized accordingly but 'bilinear' shows noisy image, any clues? A weighted average of the attributes (color, transparency, etc.) Okay, so now lets start coding to implement it. Case 2 and 3: When either one of them is an integer. Following this: The true area method is only implemented for the cases where we are not enlarging the image. We will implement the algorithm in python3 and use Numpy. Since I want to resize an image to a larger size, I want an interpolation method that minimizes artifacts and/or aliasing. Last time we have 0.4 left to be filled up. So I wrote this article to help others who may be also wondering what INTER_AREA does. What does xofs contains? Create a User-Defined Function to Implement Bilinear Interpolation in Python ; Use the scipy.interpolate.interp2d() to Implement Bilinear Interpolation in Python ; A Linear Interpolation comes into use for curve fitting with the help of linear polynomials. This happens when either x or y is an integer resulting in q=0. And then the next three are 27, 30, 33. Let If we had first performed the linear interpolation in the y direction and then in the x direction, the resulting approximation would be the same. Does aliquot matter for final concentration? I tested on these interpolation method, for both combination, shrinking and enlarging. Here is the final code to resize images using Bilinear Interpolation: Well, thats it. If you are enlarging the image, you should prefer to use INTER_LINEAR or INTER_CUBIC interpolation. However, when scaling up an image by a non-integral scale factor, there are pixels (i.e., holes) that are not assigned appropriate pixel values. A Computer Science portal for geeks. 66: 67: Returns: 68 ~numpy.ndarray: A resize array in CHW format. One can image a 1D image in the following way shown in Figure 4. The variable is named so, because a family of functions utilising parallel computing will be called. If you are shrinking the image, you should prefer to use INTER_AREA interpolation. The obvious extension of bilinear interpolation to three dimensions is called trilinear interpolation. cv2 resize interpolation methods Published by chadrick_author on November 14, 2018 INTER_NEAREST - a nearest-neighbor interpolation INTER_LINEAR - a bilinear interpolation (used by default) INTER_AREA - resampling using pixel area relation. def bl_resize(original_img, new_h, new_w): #Estimate the pixel value q using pixel values of neighbours. There are several editing tools that we can use to resize any image to any desired size. Computer Vision Enthusiast | Experienced in Deep Learning. Should I use PyrDown before Resize for a better result? Interpolation of pixel values. Image that we are assigning values to each position, and at each position, the maximum amount we can assign is 1. Resizing by Specifying Width and Height In this first example, let's resize the image by specifying a new width and height that will downscale the image. When would I give a checkpoint to my D&D party that they can return to if they die? These indices are the offsets in x direction and y direction, such that they form a window for each channel, and the number of pixels in this window equals area. But looking the return from zz in bilinear_interp function the value is correct. For results I picked maximum and 2nd maximum psnr and calculated the count. Find centralized, trusted content and collaborate around the technologies you use most. However, I am not entirely sure what is the best practice, or what I should look for when resizing an image. To resize an image, OpenCV provides cv2.resize () function. 6. Example #1 After that, we have another 5.6 to divide. With this window, we sum the values of the pixels within it, and then divided by area. Is it illegal to use resources in a university lab to prove a concept could work (to ultimately use to create a startup)? And after enlarging I calculated psnr with orignal image. Asking for help, clarification, or responding to other answers. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Apart from that, if youre coding there are plenty of libraries available for every programming language where you can resize an image with just a single line of code without worrying about the details. We take that amount from the new 5.6, as if making the previous 0.6 to be 1. When the output image is larger than the input image in either width or/and height. [ But when the image is zoomed, it is similar to the INTER_NEAREST method. To learn more, see our tips on writing great answers. We do not currently allow content pasted from ChatGPT on Stack Overflow; read our policy here. Tested in Anaconda and Python 3.7 . Given four neighboring image coordinates (these can be the four nearest neighbors of f [ a ( n )]), then the geometrically transformed image g ( n1, n2) is computed as (3.47) which is a bilinear function in the coordinates ( n1, n2 ). Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. When the output image is not larger than the input image both in width and height: If width and height are shrinked by half, and the number of channels is not 2, then, If width and height are shrinked by half, then. For a row of pixels, this can be seen from Figure 3, where different colors represent which pixels are included each time the window moves. , Solving for the linear function, we then have the expression of (1). Hence, I am assuming that you are already familiar with the concept of bilinear interpolation. Making statements based on opinion; back them up with references or personal experience. Its values range from 0 to 255. 8. This makes the image occupy less space in the disk. In the next step, we create an empty array named. For scale_image_BL(image, scaling_factor) to work, simply include : Thanks for contributing an answer to Stack Overflow! By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. affine) along lines parallel to either the x or the y direction, equivalently if x or y is held constant. Since you have no information but the mean of the block represented by the new subpixels, you seem to have a model in mind how they should look like. Figure 5 shows the coefficients for the left pixel for 100 dxs when the output image width is two times of the input image. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Below is nearest neighbour. This is exactly what we need to do when resizing an image. I guess different interpolation methods are "best" in different aspects, and so that was part of my question. Better way to check if an element only exists in one array. Tried to use np.ceil, np.floor, np.round and plain astype ('uint8'), but none returned perfect results matching OpenCVs. if (x_ceil == x_floor) and (y_ceil == y_floor): https://www.youtube.com/watch?v=hpqrDUuk7HY&list=PLjMXczUzEYcHvw5YYSU92WrY8IwhTuq7p&index=3&t=3074s. However, this is not the behaviour of OpenCVs resize. However, if youre not, I have your back. This is undesirable, since the resized array is supposed to still represent an image. Along any other straight line, the interpolant is quadratic. I was concerned, however, that I might be misusing the cubic interpolation method because of the negative values I had encountered. During the calculation of the two positions to interpolate between, say x1 or x2 in the bi-linear interpolation, python was returing 0 for simple division such as 1/2, and not 0.5, thus there weren't always two points to interpolate between resulting in the NN-type output. What does it mean by using pixel area relation? This is what I see when I try to shrink an image: Well, this is not what we want. No account yet ? The result of bilinear interpolation is independent of which axis is interpolated first and which second. The input/output scales in both width and height are integers: INTER_AREA is the boxed/window resampling. '''. The first equation comes from the requirement that the left boundaries of the input and output images have the same coordinates. Does Python have a string 'contains' substring method? The Bilinear Interpolation is an extension of Linear Interpolation that is utilized to interpolate functions of any two given variables . The following are 30 code examples of cv2.INTER_CUBIC () . Open the image using cv2.imread () We will upscale and downscale the images using cv2.resize () In the cv2.resize () function we will use different interpolation methods by passing them in that opencv function. This true area works in the following way. And the weight values vary linearly with the distances. [1], An alternative way is to write the solution to the interpolation problem as a multilinear polynomial, where the coefficients are found by solving the linear system. The MATLAB code for this mapping is written as. cv2.resize(src, dsize[, dst[, fx[, fy[, interpolation]]]]) where. However, INTER_AREA is relatively mysterious, as the document of OpenCV describes it in the following way: resampling using pixel area relation. In order to find the spline representation, there are two different ways to represent a curve and obtain (smoothing) spline coefficients: directly and parametrically. The solution can also be written as a weighted mean of the f(Q): where the weights sum to 1 and satisfy the transposed linear system. . On the other hand, if y is an integer, y_floor and y_ceil will have the same value as y. Consequently, we will get non-zero values for q1 and q2 but q will be 0 since y = y_floor = y_ceil. The numbers are the indices. BiCubic_interpolation = cv2.resize (img, (img.shape [1]*2,img.shape [0]*2),interpolation=cv2.INTER_CUBIC) . img = cv2.cvtColor(img, cv2.COLOR_RGB2BGR) img = img.transpose(2, 0, 1) img = torch.FloatTensor(img, device=self.device) img = func.imnormalize(img) img = img.unsqueeze(0) return img I don't want resize the images with opencv and convert them to Tensor. We will implement the algorithm in python3 and use Numpy. Nor is MATLABs imresize. If x and y represent a regular grid, consider using RectBivariateSpline. Approaching The Quora Insincere Question Classification Problem, Effects of Multi-collinearity in Logistic Regression, SVM, RF, Quality Metrics for NLU/Chatbot Training Data / Part 2: Embeddings, What is a neural network and how can I teach it to race a car? Bilinear interpolation is one of the basic resampling techniques in computer vision and image processing, where it is also called bilinear filtering or bilinear texture mapping. If I opt to use cv2.INTER_CUBIC, I may get values outside this range. In this we use cv2.INTER_LINEAR flag as shown below 1 bilinear_img = cv2.resize(img,None, fx = 10, fy = 10, interpolation = cv2.INTER_LINEAR) Output: This produces a smooth image than the nearest neighbor but the results for sharp transitions like edges are not ideal because the results are a weighted average of 2 surrounding pixels. Connect and share knowledge within a single location that is structured and easy to search. Some rounding issues in values (when comparing to OpenCV's result). If we choose a coordinate system in which the four points where f is known are (0,0), (1,0), (0,1), and (1,1), then the interpolation formula simplifies to, Alternatively, the interpolant on the unit square can be written as. The second is that a distance of inv_scale_x in the output image coordinate system should be 1 in the input image coordinate system. However, I am guessing youre here because you are probably curious about what goes on behind the scenes when you resize an image and youd like to implement the resizing algorithm from scratch to understand it better. It is still similar to the integer case. This method can handle more complex problems. Since this is linear interpolation, to get the linear function, we need two equations. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Ready to optimize your JavaScript with Rust? We do not currently allow content pasted from ChatGPT on Stack Overflow; read our policy here. This algorithm reduces some of the visual distortion caused by resizing an image to a non-integral zoom factor, as opposed to nearest-neighbor interpolation, which will make some pixels appear larger than others in the resized image. Should teachers encourage good students to help weaker ones? You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. The result is the pixel value of the output image. Asking for help, clarification, or responding to other answers. Just make stuff, not even perfect and move on ! Graeme Borland, 14 Lessons Learned from my first Kaggle Competition, The BrailleBaseline System Proposal (|::), 5 More Python Projects That Can Be Built Under 5 Minutes. Alternatively, a projective mapping between a quadrilateral and the unit square may be used, but the resulting interpolant will not be bilinear. cv2.INTER_CUBIC: This option is slow but more efficient. def resizeImage (name) : img1 = Image.open(name) old = np.asarray (img1) scale_x and scale_y, however, are original image width over output image width, and original image height over output image height. INTER_AREA is a bilinear interpolation with coefficients (1, 0). Do you have any evidence supporting your claim? I think you should start with INTER_LINEAR which is the default option for resize() function. 1 Whats wrong in the following cpp Bucubic interpolation code for Image Resizing, Image Processing: Algorithm Improvement for 'Coca-Cola Can' Recognition, caffe/digits: code -11 error when using python layer with cv.resize, Differences between OpenCV image processing and tf.image processing, How to convert float16 to uint8 in Python for EXR files, CV2 resize gives erroneous results randomly when used with nearest neighbor interp, Best Interpolation for grayscale segmentation mask. I have a numpy array that I wish to resize using opencv. To help with explanations, we mention some variables used in the source code: inv_scale_x and inv_scale_y are output image width over original image width, and output image height over original image height, respectively. I also wanted to include the 2nd maximum. Figure 6 shows the coefficients for the left pixel, calculated at 100 dx positions, with a inv_scale_x being 5.6: Observe the pattern. How can I remove a key from a Python dictionary? Central limit theorem replacing radical n with n. Why was USB 1.0 incredibly slow even for its time? We can see this with a simple test: If inv_scale_x or inv_scale_y is not an integer, then the interpolation coefficients are no longer just 1 and 0. Bilinear interpolation on images stored as Python Numpy ndarray. How to upgrade all Python packages with pip? Display all the rotated image using cv2.imshow () Exit window and destroy all windows using cv2.destroyAllWindows () Example Code: Machine learning in Unity 3d, Neural Network: How it works and its industry use cases. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. In fact, the largest possible value is 0. In our example, area = 9. Rotated image Resizing images. Then after assigning another 5 ones, we have only 0.2 left. 48: If :mod:`cv2` is installed, this legacy uses the implementation in: 49:mod:`cv2`. Example #1 double scale_x = 1./inv_scale_x, scale_y = 1./inv_scale_y; # Create a numpy array, pretending it is our image, fx = (float)((dx+0.5)*scale_x - 0.5); // (1). It is used as follows: image = cv2.resize(image, dsize=(new_height, new_width), interpolation=cv2.WARP_INVERSE_MAP) With this article at OpenGenus, you must have the complete idea of Different Interpolation methods in OpenCV. If we are shrinking the original image, i.e., the final image is smaller than the original in both width and height, then the algorithm checks if the size of the original image is a multiple of that of the final one. To estimate the pixel value in the new array we need to map its coordinate values back into the original image array. Then each row of the image has 27 pixels, taking account of 3 channels. Does integrating PDOS give total charge of a system? Weights between 0 and 5 are suitable. In this case, those holes should be assigned appropriate RGB or grayscale values so that the output image does not have non-valued pixels. Another pointer to array of ints ofs points to an array of area number of indices. Bilinear interpolation is a method for two-dimensional interpolation on a rectangle. A tag already exists with the provided branch name. 'bilinear' mode output: Recently Im studying computer vision, and I came across the resize function in OpenCV. Hence, now we calculate the coordinate values for the 4 neighboring pixels. Currently the two images look identical. Inside the function, we need to get the dimensions of the original image which can be obtained using . Other backends will default to 'antialiased'. In (1), the fx is the floating-point pixel index of the input image in the x direction, whereas in (3), the fx is the interpolation coefficient for the right pixel in the x direction (i.e., the interpolation coefficients are the pair 1-fx and fx). I'm trying to evaluate the quality of image provided by implementing nearest neighbour and bi-linear interpolation to resize an image. Bilinear interpolation produces a smoother interpolation than does the nearest neighbor approach. To learn more, see our tips on writing great answers. For the bilinear method, assuming we consider a 1D image for simplicity, the interpolated pixel value is a weighted average of the two original neighbourhood pixels. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. interpolation = cv2.INTER_CUBIC); img_c = cv2.resize(img_b, (w, h), interpolation = cv2.INTER_CUBIC); This produces noticeably sharper images than the previous two methods and . Name of poem: dangers of nuclear war/energy, referencing music of philharmonic orchestra/trio/cricket. In general, you can use functions from the math (sin, cos, etc) library. This implementation is faster than the implementation in . What does "best" in your context mean? Resizing an image needs a way to calculate pixel values for the new image from the original one. Here, cbuf contains the actual coefficients, where the first applies to the left pixel, and the second to the right pixel. rev2022.12.11.43106. So lets get started. You can use OpenCV to read, write and display resized images. With these additional checks in the form of if/else loops we can be sure that no pixel will be wrongly assigned 0 value when x and y are integers. There are several interpolation techniques that can be used when resizing images such as Nearest Neighbour Interpolation, Bilinear Interpolation, and Bicubic Interpolation. an example for values outside of range using INTER_CUBIC: Edit: As berak pointed out, converting the type to float (from int64) allows for values outside the original range. We can see that fx cannot be larger than 1. If so, then a boolean variable is_area_fast will be set to true. Otherwise: INTER_AREA is a bilinear interpolation with slightly more complicated coefficient values. 5. Preserve Aspect Ratio (height to width ratio of image is preserved) Downscale (Decrease the size of the image) You may also want to check out all available functions/classes of the module cv2 , or try the search function . In the end, I decided to read the source code myself. How do I access environment variables in Python? It is my understanding that using INTER_AREA is valid for down-sampling an image, but works similar to nearest neighbor for upsampling it, rendering it less than optimal for my purpose. Thats it! By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. INTER_CUBIC a bicubic interpolation over 44 pixel neighborhood, INTER_LANCZOS4 a Lanczos interpolation over 88 pixel neighborhood. Resizing modern-day images, that are very high in resolution, using this code will take some time as its runtime complexity is O(n) because of the two nested for loops. Irreducible representations of a product of two groups. The weight of each pixel is the proportion that is included times 1/area. F The code for calculating the coefficients in the x direction for the bilinear method in OpenCV is, for each pixel index dx of the output image. Is this an at-all realistic configuration for a DHC-2 Beaver? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Should I use INTER_CUBIC (and clip), INTER_AREA, or INTER_LINEAR? Bilinear interpolation considers the closest 2 2 neighborhood of known pixel values surrounding the unknown pixel's computed location. Turns out the images with lot of texture/abstraction gave highest psnr using CUBIC. Suppose our original image has a width of 9 pixels. 19/204 has the highest psnr and 158/347 have the 2nd highes psnr using AREA + CUBIC. To fill in the pixel values of the empty array we will iterate through the pixels using 2 for loops that run along the 2 dimensions. The output/input scales in both width and height are integers: INTER_AREA is a bilinear interpolation with coefficients (1, 0). Almost got there except for two things: First pixel [0] [0] is weirdly set as 0. Unlike other interpolation techniques such as nearest-neighbor interpolation and bicubic interpolation, bilinear interpolation uses values of only the 4 nearest pixels, located in diagonal directions from a given pixel, in order to find the appropriate color intensity values of that pixel. To avoid this issue, we just need to add some additional checks in the form of if/else loops before calculating q1, q2, and q values to handle such cases. Recall that to estimate a pixel value using Bilinear Interpolation we need the values of 4 neighboring pixels from the original image. CGAC2022 Day 10: Help Santa sort presents! Cubic interpolation is computationally more complex, and hence slower than linear interpolation. Quite intuitive and straightforward, isnt it? It may be a preferred method for image decimation, as it gives moire-free results. Note, also, that the input array "a" is only 3x3, which is too small for the INTER_CUBIC's 4x4 patch. PSE Advent Calendar 2022 (Day 11): The other side of Christmas. "Extraction of the Level Lines of a Bilinear Image", Bilinear interpolation definition (popular article on www.pcmag.com, "BL-ALM: A Blind Scalable Edge-Guided Reconstruction Filter for Smart Environmental Monitoring Through Green IoMT-UAV Networks", "Web tutorial: Digital Image Interpolation", https://en.wikipedia.org/w/index.php?title=Bilinear_interpolation&oldid=1119799277, This page was last edited on 3 November 2022, at 13:36. 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