Glossary

The neighborhood-weighted-sum operation, defined for a 2D image and kernel.

A complex value F(u,v) for every row-frequency/column-frequency pair, computed from every pixel.

Giving every pixel its own threshold, computed from its own local neighborhood, instead of one shared global value.

A linear map plus a translation, combining any mix of scale, rotate, reflect, shear, and shift.

A fourth per-pixel channel recording opacity.

Keeping only frequencies whose distance from the origin falls within a chosen ring.

An edge-preserving smoothing filter weighting neighbors by both spatial closeness and intensity similarity.

A weighted average of the four pixels surrounding a fractional source coordinate.

An image with exactly two legal pixel values.

The number of bits used to store each channel's value per pixel.

A five-stage pipeline producing thin, well-localized, reliably-detected edges.

One of the stacked grayscale-shaped layers that make up a multichannel image.

A device-independent, perceptually uniform color space defined relative to a white point -- equal numeric distance tracks equal perceived difference.

Capping a computed value into the legal representable range.

The subtractive ink color model -- cyan, magenta, yellow, plus a separate black channel extracted from what all three share.

The set of colors a specific device (a display or a printer) can actually produce.

Classifying a pixel by testing its hue against a target range, rather than testing raw intensity.

Blending a foreground image onto a background using the foreground's alpha channel.

A maximal set of foreground pixels all reachable from one another under a chosen adjacency rule.

The rule deciding which neighboring pixels count as "touching" when chaining edge or region pixels together.

A linear point operation mapping an observed value range onto the full display range.

Convolving two images in space is exactly pointwise multiplying their DFTs in frequency.

A location where the local image structure constrains position in every direction at once, not just one.

The n x n matrix of how pixel POSITIONS co-vary across a dataset of images -- distinct from a single image's own pixel-value covariance.

A running total of the histogram up to a given intensity.

A clean image blurred by a PSF, then hit with additive noise.

Marking a pixel foreground if the structuring element's footprint touches any foreground pixel at all.

Rewriting a small block as a sum of real-valued cosine basis patterns of increasing frequency.

The two finite-difference approximations to an image's partial derivatives.

A second-derivative convolution kernel measuring how much a pixel differs from its neighborhood.

The ratio between the brightest and darkest representable (or measured) value.

An eigenvector of an image dataset's covariance matrix, reshaped back into image form.

Assigning shorter codes to more frequent symbols, chasing the Shannon entropy bound.

Keeping a pixel only where the structuring element fits entirely inside the foreground.

A numeric vector describing the local image patch around a detected keypoint, built to survive rotation, scale, and lighting change.

Matching a descriptor to its Euclidean-nearest neighbor in a second image, rejected as ambiguous when a second candidate is nearly as close.

In compositing, the layer drawn on top (foreground) versus the layer it covers (background).

Multiplying a DFT by a mask that keeps frequencies within (or outside) a cutoff radius.

A tunable point operation, f(v) = v^gamma, that lightens or darkens depending on the exponent.

A smoothing kernel whose weights follow a 2D bell curve, tapering from the center.

Convolving an image with the Gaussian kernel, with strength controlled by sigma.

One fixed cutoff T applied to every pixel in an image, foreground below it and background above it.

The iterative update x <- x - eta*grad f(x), the general tool for minimizing an objective with no closed form.

The edge-strength number and edge-orientation angle combined from Gx and Gy.

An image storing one intensity value per pixel, with no color information.

A response function R = det(M) - k*trace(M)^2, built from a window's own gradient products, that classifies a pixel flat/edge/corner with no eigensolver required.

Unsharp masking generalized with a boost factor that also amplifies the original image.

A point operation that spreads out an image's intensity values to use the full range as evenly as possible.

Reshaping a source image's histogram to resemble a chosen target histogram.

Two structuring elements at once -- a foreground template and a background template -- to locate an exact local pattern.

Appending a constant 1 to a 2D point so translation becomes an ordinary matrix multiply.

A 3x3 matrix with a position-dependent perspective divide, able to bend straight lines.

Hue, saturation, lightness -- the same hue/saturation idea as HSV, but brightness measured as the midpoint between the RGB extremes.

Hue, saturation, value -- color split into which hue, how vivid, and how bright the brightest channel reads.

A two-threshold, connectivity-based rule for accepting or rejecting edge pixels.

Recovering a cause from an effect when the forward model destroys or barely preserves some information.

An R x C image, flattened row-major into a single n-pixel vector, exactly reversible.

An image's height and width, in pixels.

A count of how many pixels take each possible intensity value.

Data describing an image (dimensions, bit depth, capture settings) stored alongside its pixel grid.

The point operation f(v) = 255 - v, flipping the brightness scale end for end.

Dividing the degraded spectrum by the PSF's own frequency response to estimate the clean image.

Resampling by asking, for every output pixel, where it came from in the source.

The standard six-step lossy image compression pipeline built from this chapter's own tools, plus Chapter 11's YCbCr conversion.

Clustering pixel intensities into k groups by alternating nearest-centroid assignment and centroid recomputation.

The small grid of weights convolution or correlation slides across an image.

Gaussian smoothing followed by the Laplacian, locating edges at sign changes rather than magnitude peaks.

A point operation that expands dark values and compresses bright ones.

How much of each frequency is present in an image, independent of where it sits.

A neighborhood operation replacing each pixel with the median of its neighborhood.

Dilation minus erosion, isolating the outline of a shape.

A uniform streak-shaped PSF produced by a point of light moving during a single exposure.

A new pixel value computed from a whole local window of input pixels, not just one.

A precise mathematical description of how corruption is added to a captured image.

Thinning a gradient-magnitude image to single-pixel width by keeping only local maxima along the gradient direction.

Zeroing one exact frequency bin (and its conjugate) to remove a single periodic pattern.

The fastest spatial pattern a given pixel spacing can represent without aliasing.

Erode-then-dilate to remove small bright noise; dilate-then-erode to fill small dark gaps.

The per-pixel apparent motion (u,v) between two consecutive frames, solved from the same structure tensor Sections 1-2 already built.

Computing the optimal global threshold automatically by maximizing the separation between two intensity classes.

Extending an image's border with extra pixels so the kernel window doesn't run off the edge.

Where, spatially, each frequency component is positioned.

One sample of a scene's brightness (or color) at a single grid location.

A known source point paired with the destination it should map to.

A new pixel value computed purely from the old value at the same location.

A system's own response to a single infinitesimal point of light, treated as a convolution kernel.

An image's own coefficient along one eigenimage direction -- what gets kept, instead of raw pixels, under PCA-based compression.

Assigning a color to each grayscale intensity purely for display -- the underlying data stays a single scalar per pixel.

Mapping a value from a larger or continuous range onto one of finitely many representable levels.

Dividing a DCT coefficient by a perceptually-weighted step size and rounding -- the one lossy step in JPEG.

Fit a model to a random small sample, count inliers under it, repeat, and keep the model with the most support.

The three kinds of slack a raw image carries -- correlated neighbors, unequal symbol frequencies, and detail a human eye can't perceive.

Growing a segmented region outward from a seed pixel, admitting each neighbor only while it stays close to the region's own running mean.

Solving a degradation's inverse problem by penalizing implausible solutions, not just fitting the data.

Computing a usable pixel value at a non-integer source coordinate.

A color image storing three independent intensity values (red, green, blue) per pixel.

Overshoot and undershoot near sharp edges, caused by an ideal hard-cutoff filter's negative side-lobes.

Turning every point about the origin by a fixed angle.

Replacing a run of consecutive identical symbols with one (value, count) pair.

Measuring a continuous scene only at discrete, evenly spaced grid locations.

Multiplying every coordinate by a fixed factor about the origin.

A 2D kernel that factors into two 1D kernels, computable as two cheaper 1D passes.

The standard keypoint descriptor built from a 4x4 grid of 8-bin gradient-orientation histograms around a detected keypoint.

A shape's thin, one-pixel-wide medial axis, produced by repeated erosion.

Named 3x3 kernels approximating the image gradient with built-in perpendicular smoothing.

How much physical scene area one pixel covers.

The number of pixels a kernel window moves between consecutive output positions.

A small 0/1 array with a defined origin, slid across a binary image to define every morphological operation.

Sliding a small known patch across a search image and scoring every position by SSD or normalized cross-correlation.

A point operation mapping every pixel to one of two values based on a cutoff.

Image minus opening highlights small bright features; closing minus image highlights small dark ones.

Penalizing the sum of absolute pixel-to-pixel differences instead of squared pixel magnitudes -- edge-preserving, with no closed form.

Shifting every point by the same fixed offset.

A sharpening recipe -- blur, subtract to isolate detail, scale, add back.

Treating pixel value as elevation and flooding outward from local minima, building a dam wherever two basins would otherwise merge.

A regularized inverse filter that damps unreliable frequencies toward zero instead of dividing by them.

Luma (brightness-like) separated from two chroma (color-difference) channels, the basis of video and JPEG chroma subsampling.