2D Image Convolution

Implement a 2D image convolution operation in valid mode, which involves sliding a kernel over an image to generate a feature map. This process is fundamental in Computer Vision as it enables the extraction of relevant features from images by applying a set of learnable filters.

The concept of convolution is based on the idea of scanning an image with a smaller matrix, known as a kernel, to compute feature values at each position. The kernel is slid over the entire image, and at each position, the element-wise product between the kernel and the overlapping image region is computed, followed by summation of these products. The resulting feature map has a size of $(H - kH + 1) \times (W - kW + 1)$, where $H$ and $W$ are the dimensions of the image, and $kH$ and $kW$ are the dimensions of the kernel.

Here are the steps to perform the convolution:

1. Initialize an empty output matrix with dimensions $(H - kH + 1) \times (W - kW + 1)$.
2. Slide the kernel over the image, scanning each valid position.
3. At each position, compute the element-wise product between the kernel and the overlapping image region.
4. Sum up the products to obtain the feature value at that position.

This technique is widely used in image processing and analysis applications.