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Computer graphics creates visual representations from geometric models and numerical data. Vector graphics store shapes and drawing instructions, while raster graphics store an array of pixels. A drawing may use both: a geometric object can be rendered into a raster image and then combined with existing image data.

For example, three points specify a triangle. A perspective projection maps its geometry into a camera view, and rasterization determines contributions to output pixels. Their values can depend on a color model, surface response and illumination; ray tracing provides another way to determine visible surface interactions.

The stored representation and the sampled output answer different questions. A smooth geometric boundary can cross a pixel footprint, so choosing only one sample may introduce aliasing. Raster sampling and reconstruction makes that loss of detail explicit. Image processing then transforms an existing image, while computer graphics can generate one from a geometric description.

A Gabor filter has a kernel formed by multiplying a Gaussian function by a sinusoid or a complex oscillation. In two-dimensional image processing, its orientation and spatial frequency select local image structure; evaluating the kernel's translated dot product with an image is spatial filtering. The real even example under signed spatial filter model of a simple cell uses a cosine.

There is experimental motivation for this family without making every simple cell an exact Gabor filter. Jones and Palmer fitted two-dimensional Gabor filters to measured spatial and spectral response profiles of simple cells in cat cortex and compared independently estimated parameters as a test of spatial linearity. Their reported residuals supported the approximation in that dataset. The chosen parameters and orientation tuning curve in this article are not extracted from their measurements. ^[ref]

Georges Matheron was a mathematician who developed geostatistics from problems of estimating mineral resources using spatially distributed measurements. His work put kriging and spatial variability into a systematic probabilistic framework. He also developed mathematical morphology with Jean Serra, connecting geometric operations on sets with image processing.^[ref] In kriging, nearby measurements are combined using weights determined by a model of spatial dependence. The point is to account for both proximity and redundancy: many closely clustered observations need not contain as much new information as equally many well-separated observations.

A mathematician.^[ref]

Image compression applies data compression to pictures, usually represented by raster images. Nearby pixels often have related shades; an encoder can exploit that structure. A flat region invites run-length encoding, while lossy block averaging trades fine detail for fewer stored samples. The choice depends on whether exact pixel values matter and on the patterns in the image.

Lossless source coding recovers the encoded pixel values exactly, including sharp text or numerical image data. Lossy compression preserves an approximation and can remove features that later image processing might need. A visually smooth result is therefore a different promise from exact recovery. Neither method has a universal compression ratio: the chosen file format, its file header and the particular image all matter.

PNG is a real format with lossless source coding of its encoded image data. Its specified compression uses Deflate on reversibly filtered rows, rather than our toy RLE format. The lossy block averaging example is also a teaching format, not a description of PNG. A lossy preprocessing step followed by saving as PNG preserves the already changed pixels, not the earlier original.^[ref]

Image processing transforms recorded image signal data to remove noise, recover detail or extract structure. Variational image processing describes desired reconstructions through energies, while diffusion image processing describes filtering through evolution equations.

A grey-value image signal is a scalar function on an image signal domain or an array of pixel values. Continuous image processing models use spaces such as $L^2$, Sobolev spaces or the BV space, while discrete models use finite-dimensional arrays. The chosen representation distinguishes smooth transitions, noise and image edges.

M. D. Morris, or Michael D. Morris, is a chemist whose research connects Raman spectroscopy and chemical imaging with the composition and mechanics of bone and other tissues. His University of Michigan profile describes both instrument development and image processing for spectroscopic contrast.^[ref]

A central idea is to retain a Raman spectrum at each sampled position instead of recording only brightness. A map of a phosphate band can then emphasize mineral, while a different spectral contribution carries information about protein. Morris and W. F. Finney also studied how bone spectra respond during controlled elastic loading.^[ref]

As an original two-channel example, suppose reference responses for mineral and an organic component give measured intensities $I_1=2a+b$ and $I_2=a+3b$. Measurements $(I_1,I_2)=(5,5)$ yield $a=2$ and $b=1$ by solving the linear system. These are model response coefficients, not automatically mass fractions: quantitative composition additionally requires suitable reference specimens and measurement calibration. The example shows why spectral information can separate contributions that a single brightness image mixes.

For foreground set $A$ and structuring element $B$, morphological dilation is their Minkowski sum:Equivalently, place a translated copy of $B$ at each foreground position and take their union. For $A=\{0,2\}$ and $B=\{0,1\}$, the result is $\{0,1,2,3\}$, connecting the separated input points.

In image processing, morphological dilation can enlarge bright regions or bridge small gaps. The grayscale version for a flat footprint takes a local maximum, with the footprint reflected according to the stated offset convention.^[ref] Asymmetric footprints make reflection conventions visible; symmetric disks hide that distinction. Morphological dilation alone generally enlarges a region, whereas morphological opening combines it with morphological erosion.

OpenCV is a software library for computer vision and image processing. Its camera-geometry tools connect observed pixel coordinates to models of imaging, including camera calibration, correction of lens distortion, stereo rectification and three-dimensional reconstruction.^[ref]

A checkerboard calibration target supplies known geometry that can be observed from several camera positions. Fitting the model compares detected image points with projected target points. The resulting reprojection error measures agreement in the image, rather than independently confirming every physical dimension of the reconstructed scene.

A simple perspective projection illustrates the distinction: in $u=fX/Z$, replacing $X$ and $Z$ by $kX$ and $kZ$ for $k>0$ leaves $u$ unchanged. This scale ambiguity of perspective projection means that image agreement alone cannot verify a chosen unit of length. A camera baseline or a target of known size supplies additional metric information. Using the library well therefore includes checking geometric assumptions and units, alongside the numerical fit.

Optical character recognition converts pictures of written or printed text into encoded text. The input is an image of marks; the output is a sequence of characters that can be searched, copied or processed as text. Merely storing a scanned page as a raster image does not perform this recognition.

A typical system must locate text regions and lines, separate or jointly interpret their marks, and decide which character sequence they represent. Image processing can correct skew or improve contrast; image segmentation can identify regions and candidate boundaries. Recognition can use visual evidence together with constraints from surrounding text. These stages can fail separately: a correct symbol classifier cannot read a line that the layout analysis omitted.^[ref]

For a concrete ambiguity, the final rn of modern can resemble m in a degraded scan, producing modem. That single visual merge requires two ordinary character edits to repair: substitute the final m with r, then insert n. With six reference characters, the character error rate in this synthetic example isThe edit distance makes the scoring rule explicit; one visual mistake need not count as one character edit.^[ref]

A historical implementation illustrates the engineering choices: the 2007 description of Tesseract starts from a binary image and organizes connected outlines into text lines and words before recognition passes. That is evidence about a particular engine architecture, not a requirement that every recognizer use separate character segmentation. Accuracy depends on the images, writing system, layout and evaluation convention; fluent-looking output can still contain consequential transcription errors.

A structuring element specifies the neighborhood shape and reference position used by an operation in mathematical morphology. In binary image processing, represent it as a finite set $B$ of offsets. Morphological erosion tests where a translated $B$ fits inside the foreground; morphological dilation adds its offsets to foreground positions.

A three-by-three square uses all nine offsets around its center, while a cross uses the center and its four horizontal or vertical neighbors. They treat diagonal features differently despite having the same width. Scikit-image's morphology demonstration uses a disk-shaped footprint whose radius controls the affected scale.^[ref] The reference position matters for asymmetric shapes, and finite-image border rules must specify how neighborhoods outside the image are treated.

Wayne Rasband developed NIH Image and ImageJ, tools that make quantitative image processing available through an interactive program and extensible code. The ImageJ project's biography records forty years at the US National Institutes of Health and retirement in 2010. It dates the start of NIH Image to 1987 and ImageJ to 1997, when Rasband explored implementing the earlier program in Java.^[ref]

This progression mattered because the same recorded digital image could become input to many explicit measurements. Selecting a region of interest, applying image thresholding and measuring an area are separate operations; each makes a choice that affects the result. ImageJ User Guide by Tiago Ferreira and Wayne Rasband records the program's image representations, selections, analysis commands and scripting facilities.^[ref]

For a small original measurement example, take four stored grayscale valuesSelect values at least 128, obtaining the binary image $(0,0,1,1)$. If each complete pixel represents a rectangle of calibrated width $\Delta x=0.5\mu \mathrm{m}$ and height $\Delta y=0.5\mu \mathrm{m}$, the area from a calibrated pixel count isThe chosen threshold determines which pixels contribute; the pixel pitch determines the physical area assigned to each. An attractive display alone supplies neither of these measurement choices. The calculation assumes complete selected pixel cells and a uniform rectangular calibration; it is not a measured specimen area.

Rasband's contribution also includes maintaining a community around the software: the project profile describes improvements supplied through user feedback, bug reports, code and documentation. That process connects a general algorithm to the concrete representations and measurement conventions needed for a repeatable analysis.^[ref]