Problems

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2D Convolution (Image Filtering)

Computer Vision

Medium

Apply a CNN-style two-dimensional filter to a single-channel image. Pad every side with zeros, then slide the kernel with the supplied stride. Do not flip the kernel.

Y_{i,j}=\sum_{a=0}^{K_h-1}\sum_{b=0}^{K_w-1}X^{\mathrm{pad}}_{is+a,js+b}K_{a,b}

H_{\mathrm{out}}=\left\lfloor\frac{H+2p-K_h}{s}\right\rfloor+1

W_{\mathrm{out}}=\left\lfloor\frac{W+2p-K_w}{s}\right\rfloor+1

Here, $X$ is the image, $K$ is the kernel, $s$ is stride, and $p$ is padding. Return the output as a two-dimensional list of numbers.

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Examples

Input: image = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], kernel = [[1, 0], [0, 1]], stride = 1, padding = 0

Output: [[6, 8], [12, 14]]

Explanation: Each output is the sum along the main diagonal of its two-by-two image patch.

Input: image = [[1, 2], [3, 4]], kernel = [[1, 1], [1, 1]], stride = 1, padding = 1

Output: [[1, 3, 2], [4, 10, 6], [3, 7, 4]]

Hint 1

Build a zero-filled padded grid and copy the image into its center.

Hint 2

Use four loops for output rows, output columns, kernel rows, and kernel columns.

Requirements

Apply zero padding on every side
Slide the unflipped kernel using the specified stride
Compute one elementwise-product sum per output position
Return a two-dimensional list

Constraints

The image and kernel are nonempty rectangular lists
The kernel fits the padded image
Stride is positive and padding is nonnegative

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