Image Processing and Computer Vision: Filtering and Analysis

Vocabulary flashcards covering image filtering techniques, kernels, pyramids, and frequency analysis based on the lecture notes.

Image Filtering

The process of transforming an image by changing pixel values according to a rule that preserves or enhances specific features.

Sliding-kernel Filtering

A process where a local neighborhood, represented by a kernel, moves across the image to calculate new pixel values.

Box Filter

A filter that replaces each pixel with the average of its neighborhood, assigning equal weights to all pixels in the window.

Gaussian Filter

A smoothing filter that assigns larger weights to pixels near the center of the window and smaller weights to distant ones, producing a natural blur.

Separable Filter

A 2D filter that can be decomposed into the product of a column vector and a row vector, allowing it to be implemented as two 1D convolutions.

Convolution

A mathematical operation where the kernel is flipped horizontally and vertically before calculating the weighted sum of the neighborhood.

Cross-correlation

A process similar to convolution but uses the kernel exactly as it is, without flipping it.

Sobel Filter

A filter used to estimate image gradients and detect edges by calculating horizontal ($S_x$) and vertical ($S_y$) responses.

Median Filter

A non-linear filter that is especially effective for removing salt-and-pepper noise from an image.

Image Pyramid

A collection of images of the same scene represented at different resolutions.

Gaussian Pyramid

A structure that stores progressively smaller and smoother versions of an image, typically reduced by a factor of $M/2 \times N/2$ at each level.

Laplacian Pyramid

A structure that stores the residual details (the difference) between levels of a Gaussian pyramid, used for image reconstruction.

Aliasing

False patterns or distortion that occur when an image is subsampled without first removing high-frequency components.

Low-pass Filter

A frequency filter mainly used for smoothing or blurring by allowing only low-frequency components to pass.

Linear Shift-Invariant (LSI) Filtering

A type of filtering where each output pixel is a linear combination of neighboring pixels, and the same kernel is applied at every location.

Image Gradients

Representations of the directional change in image intensity, which are strongly related to edges and boundaries.

Derivative of Gaussian (DoG)

A filter that combines Gaussian smoothing to reduce noise with differentiation to highlight intensity transitions.

Laplacian of Gaussian (LoG)

A filter that applies a second derivative operator after Gaussian smoothing, used for detecting edges and blob-like structures.

Dilation

A morphological operation that expands bright regions in an image by taking the maximum value in a neighborhood.

Erosion

A morphological operation that shrinks bright regions in an image by taking the minimum value in a neighborhood.

Low Frequencies

Image components corresponding to smooth intensity changes and coarse image structure.

High Frequencies

Image components corresponding to rapid intensity changes, such as edges, textures, and fine details.

Valid Output Mode

A boundary handling strategy where output pixels are only computed for positions where the kernel fully fits within the image, resulting in a smaller output.

Non-separable Filter Cost

The computational cost for an image of size $M \times M$ and kernel $N \times N$, calculated as $M^2 \times N^2$.

Separable Filter Cost

The reduced computational cost achieved by splitting a 2D convolution into two 1D passes, calculated as $2M^2N$.