How do you calculate the output feature map size in a CNN?

The output feature map dimension O is computed using the formula: O = floor((W - K + 2P) / S) + 1, where W is the input image dimension, K is the kernel size (e.g., 3), P is the padding amount (0 for Valid, 1 for Same with 3×3 kernels), and S is the stride step size.

What is the difference between Valid (0) padding and Same (1) padding?

Valid padding (P = 0) applies no extra border pixels, causing the output feature map to shrink by (K - 1) pixels (e.g., a 28×28 input with a 3×3 kernel becomes 26×26). Same padding (P = 1 for 3×3 kernels) wraps the input with a 1-pixel border of zeros, preserving the spatial input resolution (28×28 remains 28×28 with stride 1) and allowing deep architectures to stack dozens of convolutional layers without losing edge information.

What are Sobel and Prewitt filters and how do they detect edges?

Sobel and Prewitt filters are 3×3 spatial gradient approximation kernels. Sobel kernels use weighted coefficients [-1, 0, 1; -2, 0, 2; -1, 0, 1] to calculate horizontal (X) gradients with central smoothing, and [-1, -2, -1; 0, 0, 0; 1, 2, 1] for vertical (Y) gradients. Prewitt kernels use uniform [-1, 0, 1] weights. When convolved with an image, these kernels yield high positive or negative activation responses along boundaries where pixel intensities transition sharply.

What is the Frobenius inner product in 2D convolution?

The Frobenius inner product is the sum of the element-by-element multiplication of two equally-sized matrices. In a 2D convolution with a 3×3 kernel K and receptive field patch R, the output scalar value is computed as: Output = sum_{m=0..2} sum_{n=0..2} (R[m, n] * K[m, n]) + bias.

Interactive Computer Vision Engine

Convolution Operation

In deep learning, convolution operations transform inputs into spatial feature maps using a sliding window and parameterized filter kernels. Explore the interactive demonstration below to master receptive fields, Sobel edge detectors, and Frobenius inner products in real time.

Technical Overview: 2D Convolution Operations in Convolutional Neural Networks (CNNs)

A convolution operation in deep learning is a spatial mathematical transformation where a learnable matrix of weights called a filter kernel (such as 3×3 or 5×5) slides across an input image. At each step, it computes the Frobenius inner product (sum of element-wise products) between the kernel and the local input receptive field window:

S(i, j) = (I * K)(i, j) = ∑_m ∑_n I(i·s + m, j·s + n) K(m, n) + b

This produces an output feature map highlighting visual structures like horizontal edges, vertical boundaries, ridges, and textures.

Output Feature Map Dimension Formula

Given an input spatial dimension W, kernel size K, padding P, and stride S, the output feature map dimension O is calculated by:

O = ⌊(W - K + 2P) / S⌋ + 1

Valid (0) vs. Same (1) Padding Modes

Valid Padding (P = 0): No border zeros are added. Output shrinks from 28×28 to 26×26 with a 3×3 filter and stride 1.
Same Padding (P = 1): A 1-pixel border of zeros surrounds the input. Output preserves spatial resolution at 28×28 with a 3×3 filter and stride 1.

Common 3×3 Convolution Kernels

Sobel Horizontal (X): [[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]] — Detects vertical intensity transitions with central smoothing.
Sobel Vertical (Y): [[-1, -2, -1], [0, 0, 0], [1, 2, 1]] — Detects horizontal intensity transitions.
Prewitt Horizontal (X): [[-1, 0, 1], [-1, 0, 1], [-1, 0, 1]] — Uniform edge detection.
Laplacian Ridge / Edge Detector: [[-1, -1, -1], [-1, 8, -1], [-1, -1, -1]] — Omnidirectional edge detector highlighting high-frequency curvature.
Gaussian Blur: [[1/16, 2/16, 1/16], [2/16, 4/16, 2/16], [1/16, 2/16, 1/16]] — Low-pass smoothing filter removing high-frequency noise.