![]() ![]() empty () x_ratio = float ( img_width - 1 ) / ( width - 1 ) if width > 1 else 0 y_ratio = float ( img_height - 1 ) / ( height - 1 ) if height > 1 else 0 for i in range ( height ): for j in range ( width ): x_l, y_l = math. `height` and `width` are the desired spatial dimension of the new 2-D array. Import math def bilinear_resize ( image, height, width ): """ We first need to find the ratios (now in two dimensions), Then we will do linear interpolation between the two interpolated values and in the height dimension,īilinearly resizing a 2-D array is very much like linearly resizing a 1-D array. We first compute the interpolated value of and in the width dimension, īilinear interpolation between four points. Suppose we have four points with coordinates, ,, and and associated valued, ,, and. Like linearly resizing a 1-D array, bilinearly resizing a 2-D array relies on bilinear interpolation, which can be broken down into linear resizing operations in (height) and (width) dimension. append ( a * ( 1 - weight ) + b * weight ) return out_array Bilinear Interpolation ceil ( ratio * i ) weight = ratio * i - low a = in_array b = in_array out_array. """ ratio = ( len ( in_array ) - 1 ) / ( size - 1 ) out_array = for i in range ( size ): low = math. ![]() Import math def linear_resize ( in_array, size ): """ Putting together, we have the algorithm for linearly resizing 1-D array: For element in array b with index i, its mapped coordinate in array a is ratio * i, and we compute the interpolation using the values of the two neighboring elements a and a. We notice that the mapping depends on the ratio of the length of “integer intervals” - in this case, it’s 4/3 (i.e. Now the question reduces to how do we map the coordinates from the new array b to the original array a. Then b and b can be computed using the Linear Interpolation approach from a, a and a, a. b and b), we can map them to the original array where they will have fractionally-valued coordinates ( 4/3 and 8/3). For those points in the new array for which we don’t have corresponding points in the original array (i.e. ![]() How do we get the values of array b? Well, it makes sense to let b = a and b = a, because they have the same coordinates. Note that we make the coordinates of the first and last element of the new array the same as their counterparts in the orignal array (i.e. Now image there is another straight line that runs parallel to it, where we place the points of the new array. Image we place the n = 5 points on a straight line, where they are spaced by a distance of 1.0. Given that we know how to do interpolation between two points, let’s consider a more general scenario: we have a 1-D array a of size n (e.g n = 5 ), and we wish to stretch or shrink the array to a differet size m (e.g m = 4), where the values in the new array b is somehow computed from the original array in a linear fashion. When moves to, its value becomes similarly, becomes when moves to. The weight for is proportional to ’s distance to (rather than ), while the weight for is proportional to its distnace to (rather than ). The Linear Interpolation computes it as a weighted average of the values associated with the two points, where the weights are proportional to the distance between and, and and. Now if we have a third point with coordinate where, how do we interpolate the values of cooridnates and at coordinate ? Let’s say we have two points on a straight line with coordinate and, and they are associated with values and. We will first discuss Linear Interpolation which is more common and easier to understand. ![]() We will also investigate how to compute the backward pass of bilinear resizing when we train a neural network which uses this operation. In this post, we will discuss the intuition behind interplation algorithms (linear or bilinear), and provide numpy implementations so you will understand exactly how they work. It is a generalization of linear interpolation which only works on 1-D array. height and width of the feature map is 1/S of that of the image, where S = 16 or 32), which must be resized back to the exact spatial dimension of the original image to provide pixelwise prediction.īilinear interpolation is an intuitive algorithm for image resizing. For example, some semantic segmentation models (like FCN or DeepLab) generate a feature map with a large stride S (i.e. Resizing an image (or a feature map) to a desired spatial dimension is a common operation when building computer vision applications based on convolutional neural networks. ![]()
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