20-Bio-B4 Robotics · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2014 — 04-Bio-B4 Digital Image Processing. Three hours, open book (any paper notes or textbooks permitted, but no calculator or computer). Six questions of equal value (20 marks each); five constitute a complete paper and only the first five appearing in the answer book are marked. All six are solved here, because this set is a study resource rather than an examination script. Every question is essay/descriptive (definitions, algorithm design, system design) except the operation-count comparison in Question 2(d), which is a short analytical calculation.
Reference texts (the books a candidate should have reviewed for this subject):
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Lossless compression re-encodes image data so that the original pixel values can be reconstructed exactly from the compressed bitstream — it removes only statistical/coding redundancy (e.g. via Huffman or arithmetic coding of pixel or prediction-residual symbols, or LZW-style dictionary methods), never information the eye would miss. It is used wherever exact-value fidelity is a legal or diagnostic requirement: medical imaging archives (DICOM), satellite/scientific imagery, and any format such as PNG or lossless JPEG/JPEG-LS.
Watershed segmentation treats the image (usually its gradient magnitude) as a topographic surface, where bright ridges are watershed lines and dark basins are catchment regions; "flooding" the surface from regional minima and building dams where floods from different basins meet partitions the image into regions, one per object. It is used for separating touching or overlapping objects — e.g. splitting clumped cells in microscopy or adjoining grains in a materials micrograph — typically after marker-controlled pre-processing to suppress over-segmentation from noise.
The wavelet transform decomposes an image into components localized in both space and frequency (scale), by repeatedly convolving with a pair of low-pass/high-pass filters and downsampling (the discrete wavelet transform), unlike the Fourier transform which localizes frequency only. It is the basis of JPEG2000 compression (energy compaction into a few large coefficients at coarse scales), multi-resolution image analysis, and denoising (thresholding small high-frequency wavelet coefficients).
RGB represents a colour as additive red/green/blue intensities and is the native format of camera sensors and displays, but its three channels are highly correlated and it does not separate colour from brightness. HSV (hue, saturation, value) re-parameterizes colour as a cylindrical hue angle, a saturation (colourfulness), and a value (brightness), which matches how people describe colour and makes colour-based segmentation/thresholding far more robust to illumination changes than thresholding RGB directly. YCrCb separates a luma channel Y (weighted brightness) from two chroma-difference channels Cr, Cb; because the eye is far less sensitive to chroma resolution than luma, YCrCb is the standard for compression and broadcast (JPEG, MPEG, digital TV), where the chroma channels can be sub-sampled (e.g. 4:2:0) with little visible loss.
Digital watermarking embeds an imperceptible (or occasionally visible) pattern into an image — typically in a transform domain (DCT/DWT mid-frequency coefficients or the LSBs of pixel values) so the mark survives ordinary processing while remaining invisible to the eye. It is used for copyright protection and ownership proof, source/leak tracing (a unique watermark per distributed copy), and tamper detection (a fragile watermark that breaks if the image is edited).
The Hough transform detects parametric shapes (classically lines, and by extension circles/ellipses) by mapping each edge pixel into a vote in a parameter-space accumulator (e.g. ρ-θ for lines) and finding the accumulator peaks, so it can find a shape even when its boundary is broken by noise or occlusion because every supporting edge pixel votes independently. It is used for lane/road-marking detection, industrial part/feature alignment, and finding circular structures (e.g. cell nuclei, coins) in noisy imagery.
Mathematical morphology processes binary (or grayscale) images with a structuring element via the basic operators erosion and dilation, and their combinations opening (erosion then dilation, removes small foreground specks and thin protrusions) and closing (dilation then erosion, fills small holes and gaps). It is used for noise removal in binary images, separating touching objects (erosion), skeletonization, and boundary extraction as a pre-processing step before the counting/segmentation tasks seen later in this paper.
