How unit 5 is examined
This unit covers binary morphology, shape representation, skeletons, polygonal approximation, recent trends and machine learning for images; no topic was asked in the supplied papers, so each is short.
Mathematical morphology: binary, dilation, erosion, opening and closing
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Definition. <mark>Mathematical morphology processes an image with a small structuring element (SE) using set operations, and its basic operations are dilation and erosion.</mark>
Key points.
- Dilation $A\oplus B$ grows objects: it fills small holes and bridges gaps.
- Erosion $A\ominus B$ shrinks objects: it removes small specks and thin lines.
- Opening $A\circ B=(A\ominus B)\oplus B$ removes small objects and smooths contours; closing $A\bullet B=(A\oplus B)\ominus B$ fills small holes.
- A cross (plus-shaped) SE dilates by one pixel in the four neighbour directions.
Simple methods of representation, signatures, boundary segments
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Definition. <mark>Representation describes a region by its boundary, and the boundary is then reduced to descriptors such as signatures and segments.</mark>
Key points.
- A signature is a 1-D function of the boundary, for example distance $r(\theta)$ from the centroid against angle $\theta$.
- Signatures are invariant to translation, and normalising $r$ gives scale invariance.
- Boundary segments split a boundary into parts, usually at the concave points of the convex hull.
- Segmenting reduces the boundary's complexity and makes each part easy to describe.
Skeleton of a region
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Definition. <mark>The skeleton (medial axis) of a region is a thin set of pixels at the centre of the region that keeps its shape and connectivity.</mark>
Key points.
- The medial axis is the set of points having more than one closest boundary point (Blum's transformation).
- Morphologically, $S(A)=\bigcup_k\big[(A\ominus kB)-(A\ominus kB)\circ B\big]$.
- Thinning algorithms remove boundary pixels iteratively without breaking connectivity.
- Skeletons reduce a region to a graph, useful for character recognition and shape matching.
Polynomial approximation
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Definition. <mark>Polynomial (polygonal) approximation represents a boundary by a polygon or polynomial curve with as few segments as possible.</mark>
Key points.
- A minimum-perimeter polygon fitted inside the boundary cells gives the tightest polygon.
- Merging fits points to a line until the fitting error exceeds a threshold, then starts a new segment.
- Splitting cuts a segment at its farthest point from the chord until every error is below the threshold.
- It reduces data and removes noise, but the choice of threshold controls the accuracy.
Recent advancement in DIP
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Definition. <mark>Recent advances in DIP are data-driven methods, mainly deep learning, that have replaced many hand-designed algorithms.</mark>
Key points.
- Convolutional neural networks (CNNs) now lead in classification, detection and segmentation.
- GANs generate and enhance images, for example super-resolution and denoising.
- Applications include medical imaging, remote sensing, autonomous vehicles and face recognition.
- Other trends are computational photography, transformers and real-time edge processing.
Machine learning for image processing application
<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Not asked since 2022</span>
Definition. <mark>Machine learning for images learns a mapping from image features to labels using training data, instead of fixed rules.</mark>
Key points.
- Classical pipeline: extract features (edges, texture, HOG), then classify with SVM, k-NN or decision trees.
- Deep learning learns the features itself: a CNN uses convolution, pooling and fully connected layers.
- Supervised learning needs labelled images, while unsupervised learning finds clusters, as in k-means segmentation.
- Good results need large datasets and care to avoid overfitting.
Last-minute revision
- Dilation grows and erosion shrinks an object.
- Opening is erosion then dilation; closing is dilation then erosion.
- Opening removes small objects; closing fills small holes.
- A signature is a 1-D function such as $r(\theta)$ of the boundary.
- The skeleton is the medial axis, the thin centre line of a region.
- Merging and splitting are the two polygonal approximation methods.
- CNNs are the main recent advance in image classification and detection.
- A GAN generates or enhances images.
- Supervised learning needs labelled images.
Memory hooks
- Dilate = Deliver more pixels; Erode = Eat pixels.
- Opening: Erode, Dilate (E before D, alphabetical for open).
- Skeleton = the spine of a shape.
- Merge joins, Split cuts.
Coverage checklist
- Mathematical morphology- Binary, Dilation, crosses, Opening and closing: no past questions.
- Simple methods of representation, Signatures, Boundary segments: no past questions.
- Skeleton of a region: no past questions.
- Polynomial approximation: no past questions.
- Recent advancement in DIP: no past questions.
- Machine learning for image processing application: no past questions.