• **Image Analogies** (Hertzmann et al. 2001): give an example pair **A → A′** (an image and its filtered/stylized version) and a new target **B**; synthesize **B′** so that *"A : A′ :: B : B′"* — learned **by patch matching** (for each B patch, find the best-matching A patch and copy its A′ counterpart). A single example teaches a filter/style — texture-synthesis machinery turned into a transfer, the **pre-deep ancestor** of neural style (cross-ref [[Deep learning]] and [[#Inpainting, texture synthesis]]).

• **color (palette) transfer** (Reinhard et al. 2001): the leanest classical method — make a target photo take on a reference's **palette/mood** by matching just the **mean and standard deviation** of each color channel. Convert both images to a **decorrelated color space** (l$\alpha\beta$ / Ruderman — axes statistically near-independent for natural scenes, so channels can be retargeted separately without cross-talk), then per channel **shift** to the reference's mean and **scale** by the ratio of standard deviations. Only **first- and second-order statistics** — no patches, no histograms — yet enough to swap a sunset's warmth onto a daylight shot. The classical, **pre-deep ancestor of neural style / color grading**: where Gatys later matches *deep-feature* second-order statistics (Gram matrices), Reinhard matches *raw-pixel* low-order statistics in a smart color space. (Forward-ref the learned / style-based color-grading successors → [[Deep learning]] and *Style transfer as image-to-image translation* below; the decorrelated transfer space ties to [[Visual processing]].)

• **two-scale tone / style transfer** (Bae, Paris & Durand 2006): transfer the **pictorial look** of a model photograph onto a target by **separating scales** — an edge-preserving **base / detail** split — and transferring the **large-scale tonal distribution** (a histogram-match of the base) and the **detail/texture** amount independently. Classic example: give a snapshot the tonal drama of an Ansel Adams print. Ties to the base–detail decomposition of [[Edge-preserving techniques]] and to histogram matching (BASIC).

• the classical takeaway: style here is **low-order statistics + patches** — global mean/variance (Reinhard), histograms, local texture, exemplar patches — matched by hand-designed pipelines. The arc rises in statistical order: Reinhard's first/second moments → histograms/patches → the deep-feature statistics below, where the learned methods replace "hand-designed statistic" with "deep-feature statistic."

• **neural style** (Gatys, Ecker & Bethge 2016): the breakthrough that **content = deep CNN features** (what is where) and **style = the *correlations* among those features**, captured by the **Gram matrix** $G_\ell=\phi_\ell\phi_\ell^\top$ at each layer. **Optimize an image** to simultaneously match the target's content features and the reference's style Gram matrices: $\min_{\hat I}\ \alpha\lVert\phi(\hat I)-\phi(I_c)\rVert^2 + \beta\sum_\ell\lVert G_\ell(\hat I)-G_\ell(I_s)\rVert^2$. Slow (an optimization per image), but it reframed style as *deep-feature statistics*. [fig-neural-style-content-style]

• **feed-forward / perceptual-loss style transfer** (Johnson, Alahi & Fei-Fei 2016): **train a network once** to produce the stylized output in a **single forward pass**, by minimizing the *same* content+style **perceptual loss** (deep-feature distance) Gatys optimized iteratively. Real-time stylization; the same **perceptual / feature loss** reappears as a training loss for super-res and as LPIPS (cross-ref [[Deep learning]]).

• **Markovian / patch-based neural style** (Li & Wand 2016): combine **MRFs with CNNs** — match style on **local neighborhoods of deep features** (a patch/Markovian style term) rather than global Gram statistics, better preserving local structure. Sits **between Image Analogies (patches, no net) and Gatys (global feature statistics)** — patches, but in deep-feature space.

• **the GAN view**: when "style" is a whole **domain** (photos↔paintings, day↔night, summer↔winter), pose stylization as **learned image-to-image translation** — a generator maps one domain's look onto another, a discriminator keeps it plausible.

• **Pix2Pix** (Isola et al. 2017): **paired** translation — when you have aligned (input, styled-output) pairs, learn the map directly with a conditional GAN. The generic "learn the map between two image domains" tool.

• **CycleGAN** (Zhu et al. 2017): the **unpaired** version — when no aligned pairs exist (you have *photos* and *Monets*, but not the same scene as both), **cycle-consistency** ($B\to A\to B$ should return $B$) lets you learn the style mapping without pairs. The workhorse for "make my photo look like X" when X is only a *collection*.

• placement: these are surveyed as *models* in [[Deep learning]] (generative image-to-image); here they're the **learned, domain-level** end of the style-transfer spectrum. Forward-ref: text-/exemplar-driven stylization with diffusion ([[Generative AI and diffusion]]) is the current frontier.

• refs: Reinhard et al. 2001 (color transfer between images); Hertzmann et al. 2001; Bae, Paris & Durand 2006; Gatys et al. 2016; Johnson, Alahi & Fei-Fei 2016; Li & Wand 2016; Isola et al. 2017 (Pix2Pix); Zhu et al. 2017 (CycleGAN).

• **the goal**: a **depiction**, not a reproduction — painterly, sketch, or cartoon, **emphasizing structure** and **suppressing clutter**. Closer to *illustration* than photography; the value is in **what's left out**.

• **the one idea — structure-aware abstraction**: keep what the eye uses (strong **edges**, **large-scale tone**, the silhouette), simplify the rest (fine texture, mid-tone noise, busy backgrounds). **L23.1** (separate the subject, commit) executed in pixels, using **L4.21** (edge-preserving) machinery.

• **intuition-first**: a cartoon = **flat color regions + bold outlines.** Flat regions come from an **edge-preserving smoother** (don't blur across edges); outlines from an **edge detector**. That two-part recipe is the whole field in one sentence.

• **the idea** (Hertzmann 1998 — *queue ref*): repaint the photo with **discrete brush strokes**, **coarse-to-fine** — big rough strokes over a heavily-blurred version, then progressively **smaller** strokes **only where** the painting still differs from the (less-blurred) reference. Detail appears where needed; flat areas stay loose. [`fig-npr-painterly-layers`]

• **the structure that makes it look good (not random daubs)**:

• **orientation**: strokes run **perpendicular to the image gradient** (along the "grain") — following a cheek's contour or a sky's flow (**L6.3**);

• **size = scale**: coarse strokes on coarse pyramid levels, fine on fine — a direct use of the **Gaussian / image pyramid** ([[Pyramids and wavelets]]);

• **curved strokes**: trace along the orientation field for long painterly strokes, stopping at edges;

• **error-driven placement**: add a stroke only where canvas-vs-reference error exceeds a threshold → the painting **converges** to the photo at the chosen abstraction level.

• **the parameters are the *style***: stroke size range, opacity, jitter, curvature, blur radius → impressionist vs pointillist vs expressionist from *one* algorithm. (The **Gaussian pyramid** sets stroke scale and the blurred references.)

• **the course p-set**: implement the **layered, gradient-following brush painter** — build the pyramid of blurred references, place oriented strokes coarse-to-fine, explore a couple of brush/parameter styles on your own photo. [`fig-npr-brush-pset`] Use the photos-from-Fredo / sourced images for the worked example.

• **the canonical real-time pipeline** (Winnemöller et al. 2006 — *queue ref*): [`fig-npr-abstraction-pipeline`]

1. **flatten regions** with a **bilateral filter** (iterated) — smooths within objects, **stops at edges** (**L4.21**), collapsing texture into flat cartoon regions; optionally **quantize** color/luminance into a few bands (the posterized look);

2. **draw lines** with a **Difference-of-Gaussians**, $D = G_{\sigma_1}*I - G_{\sigma_2}*I$, thresholded into **black ink edges**;

3. **composite**: flat quantized color **+** DoG lines = a cartoon, in real time, even on video.

• **why this *is* EDGES MATTER**: the bilateral step is literally the [[Edge-preserving techniques]] base/detail filter (**L4.21**) — here used to **destroy** detail deliberately, not enhance it. Same tool, opposite intent.

• **flow-based DoG / coherent lines** (Kang et al. 2007 — *queue ref*): plain DoG gives **broken, noisy** edges; compute a smooth **edge-tangent flow** and run the DoG **along** it → **long, clean, coherent** lines like a confident pen. [`fig-npr-flow-dog`]

• **temporal coherence** (for video): filter with motion-awareness so flat regions and lines don't **flicker** frame-to-frame.

• **eye-tracked, perceptually-guided abstraction** (DeCarlo & Santella 2002, *Stylization and Abstraction of Photographs*, SIGGRAPH): the chapter's deepest answer to *what to keep*. Instead of inferring importance from edges alone, they **record where a viewer actually looks** (an eye-tracker) and build a **hierarchical, multi-scale** abstraction that **preserves detail at the fixated, meaningful regions and simplifies everything else** — bold flat color and clean bounding contours from a segmentation hierarchy, with detail *dialed in by measured visual attention*. NPR reframed as **directing the eye**: the abstraction reads as right because it is tied to **perception**, not just to gradients (**L23.1** — separate the subject and commit). This is the model of *meaningful* (importance-driven) abstraction, and the natural complement to the bilateral + DoG pipeline above, which abstracts the frame uniformly.

• **Image Analogies** (Hertzmann et al. 2001): give one example pair **A → A′** (a photo and its hand-stylized version) and a new photo **B**; synthesize **B′** so *A:A′ :: B:B′* by **patch matching** — *learn the style from one example*. The pre-deep ancestor of neural style; developed in [[#Style transfer]] (and surveyed in [[Deep learning]]) — appearing in both by design.

• **the bridge to neural style**: classical NPR hand-codes *what to keep* (edges, strokes, flat regions); **neural style** (Gatys 2016) replaces those rules with **deep-feature statistics** (content features + Gram-matrix style), and **feed-forward** stylization (Johnson 2016) makes it real-time — the same painterly goal, the prior now **learned** (**L5.3**). Full treatment in [[#Style transfer]] / [[Deep learning]].

• **the takeaway**: across painterly strokes, bilateral+DoG cartoons, and neural style, the constant is **abstraction guided by structure** — decide what carries meaning, keep and exaggerate it, simplify the rest. NPR is **L4.21 + L23.1** turned into a rendering style.

• **the idea**: instead of strokes or edges, **partition** the image into a few large regions and fill each with a **flat color** (its mean) — *abstraction by tessellation*. Pick the tiling to respect structure: a **Voronoi / centroidal** tessellation ("**stained glass by numbers**"), a **Delaunay low-poly** triangulation seeded at salient/edge points, or **superpixels** (SLIC). Same NPR thesis — *abstraction guided by structure* (**L4.21**) — with "what to keep" carried by **region boundaries** rather than brush orientation.

• **the dial = number / shape of regions**: few large cells → bold, poster-like; many small cells → near-photographic. Edge-aware seeding keeps tiles from straddling strong contours (the [[Bilateral filtering]] / segmentation link).

• **p-set lineage**: the "stained glass by numbers" make-your-own assignment; kin to **photomosaics** ([[Slopendium/Photo collections#Photomosaics, Salavon]]) and to **graph-cut region labeling** ([[Seam optimization]]).

• **the idea**: reproduce a continuous-tone image with **discrete marks** — the classic print problem — but make the *marks themselves* expressive. Ordinary **halftoning** trades spatial resolution for tone (clustered-dot screens, **ordered dithering**, **error diffusion** à la Floyd–Steinberg); **artistic screening** (Ostromoukhov & Hersch) replaces the regular dot screen with **shaped, image-bearing screen elements** so the halftone microstructure carries a *second* picture, lettering, or texture. Tone is still right at a distance; up close the rendering is a deliberate pattern.

• **why it's NPR**: same thesis — *abstraction guided by structure* (**L4.21**) — here the abstraction lives in **how tone is quantized into marks**, not in strokes, edges, or regions. Stippling, engraving/hatching, and ASCII-art are the same move with different mark vocabularies.

• **the dial = the screen / mark set**: choice of screen element, frequency, and angle sets the style; error-diffusion vs ordered-dither sets the "texture" of the noise (blue-noise dithers look cleanest). Ties to [[Measuring and encoding color|Color technology]] (CMYK screen angles, moiré) and the perceptual reason it works (the eye's spatial averaging — [[Visual processing]]).

• **p-set lineage**: the "artistic screening" make-your-own assignment.