CSE 4227 · Prof. Kalpoma · AUST

DIP on one page

What each question type wants, which method each story word points to, every formula with a worked line, and the theory points to write. Fall 2024 papers are left out.

The paper in one look

70 marks · 3 hours

In plain wordsThree questions. Q1 asks you to explain, Q2 asks you to calculate, Q3 gives a story (a hospital, a satellite, a scanner) and asks which method fits. The same 12 methods answer all three; only the way you write changes.

question	what it wants	choice	how you write it
Q1 theory · 25	define, compare, list effects	any 5 of 6 (one per chapter)	definition → formula → 2–3 points → small sketch
Q2 math · 24	numbers: histogram, filter, compression, chain code / morphology	about 3 of 4	formula → table of every step → final grid / code → one-line comment
Q3 case · 21	a real problem; pick and justify methods	any 3 of 4	problem → method → why → steps (with equation) → result

Time: about 2.5 minutes per mark. A 7-mark case = 17 minutes. Never spend more than 20 minutes on one part.

Where marks hide: the formula line, the working table and the final labelled answer each carry marks on their own. A right answer with no table loses about half.

How everything connects

all 14 decks

In plain wordsEvery topic is one stop on the same road: take a picture, make it look better, find the object, describe its shape, store it small. Once you see the road, you know which chapter a question comes from.

1 · Capturedecks 01–03

sampling, quantization, bits, pixels, neighbours, distance

2 · Enhancedecks 04–07

point ops (negative, log, gamma, stretch, slice, bit-plane) → histogram → smooth → sharpen

3 · Find objectsdecks 08–09

edges (gradient, Laplacian, Canny) or regions (threshold, region growing)

4 · Clean shapedecks 11–12

erosion, dilation, opening, closing, boundary, hit-or-miss

5 · Describe shapedeck 10

chain code → CFD → shape number

6 · Store / colourdecks 13–14

Huffman, Golomb, LZW, RLE, RMSE · RGB, CMY, HSI

The same idea shows up twice (connect these dots)

first meeting	second meeting	the link
thresholding s = 1 if r > k (deck 04)	global / iterative threshold (deck 09), binary input for morphology (deck 11)	one cut turns gray into object vs background
contrast stretching (deck 04)	histogram equalization (deck 05)	both spread values over 0…L−1; HE does it automatically from the CDF
mean / Gaussian smoothing (deck 06)	Canny step 1, LoG (deck 08)	smooth first so noise doesn't make fake edges
Laplacian ∇²f (deck 07)	LoG / zero crossings (deck 08)	2nd derivative: thin double edges, sensitive to noise
Sobel / Prewitt gradient (deck 07)	Canny step 2 (deck 08)	1st derivative: edge strength and direction
median filter (deck 06)	salt-and-pepper case questions (Q3)	median ignores extreme 0/255 values and keeps edges
boundary β(A) = A − (A ⊖ B) (deck 11)	chain code walks that boundary (deck 10)	first find the outline, then code it
erosion (deck 11)	hit-or-miss = two erosions (deck 12)	HMT erodes the object with B1 and the background with B2
entropy H (deck 13)	Huffman L_avg (deck 13)	H is the floor: L_avg ≥ H, efficiency = H / L_avg
histogram p(r_k) = n_k/N (deck 05)	probabilities for Huffman and entropy (deck 13)	same counting table, different use
intensity I in HSI (deck 14)	gray-level methods (decks 04–06)	enhance I only, keep H and S, colours stay true

Cue words: what the question really asks

Q3 and Q1 triggers

In plain wordsCase questions hide the method inside a story. Spot the problem word, map it to the method, then justify with one line of how the method works. Learn this table and Q3 becomes matching.

Enhancement stories

you read	it means	you write / use
too dark, underexposed X-ray / MRI, details hidden in shadows	dark values squashed together	log or gamma γ < 1; or histogram equalization
washed out, too bright, aerial photo, faded	bright values squashed together	gamma γ > 1 (3.0–4.0 on the slides)
low contrast, dull, narrow histogram	values use only part of 0…L−1	contrast stretching or histogram equalization
highlight a range: tumor, bone [120, 200], water in satellite	one band of gray levels matters	gray-level slicing: give both approaches (background 0, or keep r)
huge dynamic range, Fourier spectrum	values 0 to 10⁶ won't fit 0–255	log transform
negative film, white lesions in dark mammogram	dark ↔ light swap helps viewing	negative s = L−1−r
hidden watermark, which bits matter, compress by bits	image = stack of bit planes	bit-plane slicing: top planes carry the shape
want the look of another image	target histogram given	histogram matching (specification)

Noise and sharpness stories

you read	it means	you write / use
salt-and-pepper, impulse noise, black and white dots	isolated extreme 0 / 255 pixels	median filter 3×3 (keeps edges)
Gaussian noise, grainy, random noise	every pixel slightly off	mean / weighted average / Gaussian filter (blurs a bit)
only pepper (black dots) / only salt (white dots)	one-sided impulses	max filter removes pepper, min filter removes salt
blurred, fine detail, sharpen, faded ink edges	edges too soft	Laplacian g = f − ∇²f, or unsharp masking / high-boost
find edges / outline of an organ, crack, road edge	big change in intensity	Sobel / Prewitt gradient, best: Canny
noisy image but need thin, clean, connected edges	edge detector that resists noise	Canny (smooth, gradient, NMS, double threshold, hysteresis)
straight lines: roads, lanes, fracture lines	pixels lying on a line	line masks (−1 −1 −1 / 2 2 2) or Hough transform (one line: votes in (ρ, θ))

Segmentation stories

you read	it means	you write / use
separate object from background, text from paper	two intensity groups	thresholding; iterative T = ½(μ₁ + μ₂)
uneven illumination, shadow on the document	one T can't fit everywhere	local / adaptive threshold (T from each neighbourhood)
group similar pixels from a seed point, tumor region	grow from a known pixel	region growing: \|neighbour − pixel it grows from\| ≤ T
"partition pixels depending on intensity"	the words for thresholding	thresholding (SP23 Q1(b)ii)
"groups similar pixels"	the words for region-based	region growing or split & merge (SP23 Q1(b)iv)

Shape stories (binary images)

you read	it means	you write / use
broken characters, gaps in roads, cracks to join	small breaks in the object	dilation (or closing to keep thickness)
small bright spots, specks, small particles to remove	objects smaller than the SE	opening (erode, then dilate)
small holes inside objects, reflections to fill	background specks inside the object	closing (dilate, then erode)
touching coins, count objects	thin necks join the objects	erosion to split, then count connected components
outline / boundary of roads, organ edge (binary)	the object's border pixels	boundary β(A) = A − (A ⊖ B)
find corners, end points, a fixed pattern	match object AND background	hit-or-miss A ⊛ B = (A ⊖ B₁) ∩ (Aᶜ ⊖ B₂)
recognise a shape whatever its rotation / start	describe the boundary by numbers	chain code → CFD → NCFD (shape number)

Storage and colour stories

you read	it means	you write / use
medical, legal, must not lose any detail	lossless only	Huffman, LZW, RLE, Golomb, arithmetic
many repeating patterns / colours, bitmap, fixed-length codes	the same sequences come back	LZW (dictionary, 9-bit codes)
long runs of the same value, fax, binary documents	consecutive equal pixels	RLE (value, run length)
some gray levels far more common than others	unequal probabilities	Huffman (short codes for frequent values)
small integers / prediction errors, geometric spread	small values common	Golomb G_m(n)
whole message as one number	non-block code	arithmetic coding
how good is the decompressed image?	fidelity criterion	RMSE (objective) or rating scale (subjective)
printing, ink, printer	subtractive colour	CMY / CMYK
monitor, camera, display	additive colour	RGB
segment by colour, lighting changes, describe colour like humans	separate colour from brightness	HSI (use Hue)

TrapWhen a case lists four methods (SP25 Q3(d): chain code, histogram, Hough, power-law), give each one line of what it does, one line of how it helps here, and one limitation. That is the 3-part pattern she marks.

Q3 case answers: the template and six solved stories

SP23 · F23 · SP24 · SP25 · F21 · F25 quiz

Problem (cue word) → Method → Why it works → Steps / equation → Result + one limitation

Write each case as 4–6 short lines in that order. Name the method in bold in the first line; the examiner looks for it.

SP23 Q1(b) · brain tumor pipeline2 + 2 + 3 + 2

(i) Remove noise: median filter (scan noise is impulse-like; median keeps tumor edges) or Gaussian/mean for random noise.

(ii) Partition by intensity: thresholding, g = 1 if f > T else 0; T found iteratively.

(iii) Highlight a range of values: gray-level slicing, [A, B] → L−1, others 0 (or unchanged).

(iv) Group similar pixels: region growing from a seed inside the tumor, add 8-neighbours with |difference| ≤ T.

SP25 Q3(a) · faded, unevenly lit document for OCR4 + 3 + 3

(i) Enhance: contrast stretching or histogram equalization (faded ink = low contrast) and median filter (background specks).

(ii) Laplacian over Sobel: text is thin strokes and fine detail; the 2nd derivative gives thin, sharp response and g = f − ∇²f sharpens in one mask. Sobel gives thick edges and needs two masks.

(iii) Segment: local (adaptive) thresholding, because illumination is uneven; then horizontal projection to split text lines.

SP25 Q3(c) · satellite roads with spots and gaps3 + 3 + 3

(i) Opening A ∘ B = (A ⊖ B) ⊕ B: erosion deletes spots smaller than B, dilation restores the roads' size.

(ii) Closing A • B = (A ⊕ B) ⊖ B: dilation bridges small gaps, erosion returns the road width. Use a line-shaped SE along the road.

(iii) Boundary β(A) = A − (A ⊖ B): subtract the eroded road from the road; one-pixel outline remains.

F23 Q3(b) · touching coins, small particles5 + 5

(i) Erosion with a disk SE larger than the necks: touching coins split into separate blobs; count with connected-component labeling. (Follow with dilation if size matters = opening.)

(ii) Opening with an SE just larger than the small particles: they cannot contain the SE, so erosion removes them; dilation restores the large particles to their size.

SP24 Q3(a) · salt-and-pepper only on the object4 + 4

(i) Median filter 3×3 on the object region (mask from thresholding), background untouched: impulses sort to the ends, the median ignores them, edges stay sharp.

(ii) Morphology: opening removes white (salt) specks, closing fills black (pepper) dots inside the object.

SP25 Q3(d) · bone fracture, four methods7

Power-law: γ < 1 brightens a dark X-ray so thin cracks show; limitation: also brightens noise.

Histogram analysis / equalization: spreads bone gray levels for contrast; limitation: may over-enhance soft tissue.

Hough transform: finds straight fracture lines by voting in (ρ, θ); limitation: curved cracks are missed.

Chain code: codes the bone outline; a break shows as an irregular CFD (sudden turns); limitation: noise-sensitive, needs a clean boundary.

Formulas 1 · capture and pixels

decks 01–03

what	formula	one worked line
gray levels	L = 2^k, range 0 … L−1	k = 12 → L = 4096, range 0–4095
image size	b = M × N × k bits (÷ 8 = bytes)	1024 × 768 × 12 = 9,437,184 bits = 1,179,648 bytes
nearest-neighbour zoom	position = ⌈i × old / new⌉, i = 1…new	3×3 → 5×5: ⌈0.6 i⌉ = 1 2 2 3 3 (copy those rows / columns)
city-block D₄	\|x − s\| + \|y − t\|	p(1,2), q(4,6): 3 + 4 = 7
chessboard D₈	max(\|x − s\|, \|y − t\|)	max(3, 4) = 4
Euclidean D_e	√[(x − s)² + (y − t)²]	√(9 + 16) = 5

Sampling = digitise coordinates (spatial resolution, blocky if too few). Quantization = digitise amplitude (gray-level resolution, false contouring if too few).
4-adjacent: q in N₄(p). 8-adjacent: q in N₈(p). m-adjacent: q in N₄(p), or q in N_D(p) and N₄(p) ∩ N₄(q) has no pixel in V. m removes the double paths of 8-adjacency.
Distance properties: D ≥ 0 (= 0 only if p = q), D(p,q) = D(q,p), D(p,z) ≤ D(p,q) + D(q,z). Always D₄ ≥ D_e ≥ D₈.

Formulas 2 · point transformations

deck 04

method	formula	worked line	use
negative	s = (L−1) − r	8-bit, r = 100 → 155	white detail in dark areas
log	s = c · log(1 + r), c = (L−1)/log(L)	c = 255/log 256 = 105.89; r = 50 → 105.89 × log 51 = 181	expand dark, compress bright
gamma	s = (L−1) · (r / (L−1))^γ	3-bit, r = 3: γ = 0.5 → 7 × 0.6547 = 5; γ = 2 → 7 × 0.1837 = 1	γ < 1 brighter, γ > 1 darker
min–max stretch	s = (r − r_min)(L−1) / (r_max − r_min)	[50, 150] → [0, 255]: r = 100 → 50 × 255/100 = 127.5 → 128	fill the whole range
threshold	s = L−1 if r > k, else 0	k = 127: 90 → 0, 200 → 255	binary object vs background
bit plane n	bit_n = ⌊r / 2ⁿ⁻¹⌋ mod 2 (weight 2ⁿ⁻¹)	13 = 1101: planes 4,3,2,1 = 1,1,0,1	top planes = shape, bottom = noise

Piecewise contrast stretching with (r₁, s₁), (r₂, s₂)

s =

(s₁ / r₁) · r

0 ≤ r < r₁

s₁ + (s₂ − s₁)(r − r₁) / (r₂ − r₁)

r₁ ≤ r ≤ r₂

s₂ + (L−1 − s₂)(r − r₂) / (L−1 − r₂)

r > r₂

Three special settings: r₁ = s₁ and r₂ = s₂ → identity (no change). r₁ = r₂, s₁ = 0, s₂ = L−1 → thresholding. r₁ ≤ r₂ and s₁ < s₂ in between → contrast stretching. Draw all three graphs.

Gray-level slicing, range [A, B] (F25 quiz: bone [120, 200])

approach 1 =

L−1

A ≤ r ≤ B

otherwise

approach 2 =

L−1

A ≤ r ≤ B

otherwise

r = 100 → 0 / 100 · r = 150 → 255 / 255 · r = 220 → 0 / 220. Approach 1 = binary, background gone; approach 2 = background kept.

TrapFind L first. A 3-bit image means L − 1 = 7, so gamma and log use 7, not 255. Round .5 up.

Formulas 3 · histogram equalization

deck 05 · in almost every final

p(r_k) = n_k / N → CDF = Σ p → s_k = round( (L−1) × CDF_k )

Worked (3-bit, N = 64, n_k = [8, 10, 10, 2, 12, 16, 4, 2]). Do every row like the first two:

r = 0: p = 8/64 = 0.125, CDF = 0.125, 7 × 0.125 = 0.875 → 1. r = 1: p = 10/64 = 0.15625, CDF = 0.28125, 7 × 0.28125 = 1.969 → 2.

r	n_k	p	CDF	7 × CDF	s
0	8	0.1250	0.1250	0.875	1
1	10	0.1562	0.2812	1.969	2
2	10	0.1562	0.4375	3.062	3
3	2	0.0312	0.4688	3.281	3
4	12	0.1875	0.6562	4.594	5
5	16	0.2500	0.9062	6.344	6
6	4	0.0625	0.9688	6.781	7
7	2	0.0312	1.0000	7.000	7

New histogram: add the counts that land on the same s: s = 3 gets 10 + 2 = 12; s = 7 gets 4 + 2 = 6. Total stays 64.

Equalized histogram: spread out, not perfectly flat, because levels are discrete. Write that sentence.

Matching (if asked): equalize the input → H, equalize the target → S, map each r to the z whose S is closest to its H (ties → higher S).

TrapDraw three things: the original histogram, the equalized histogram and the transformation (staircase). Each is a separate mark.

Formulas 4 · smoothing and sharpening

decks 06–07

One window, every filter. Centre pixel = 200 (a noise spike):

10	20	30
40	200	60
70	80	90

window f

1	2	1
2	4	2
1	2	1

weights / 16

filter	rule	result at the centre
mean (box)	Σ / 9	600 / 9 = 66.67 → 67
weighted average	Σ w·f / 16	1400 / 16 = 87.5
median	sort 9, take the 5th	10 20 30 40 60 70 80 90 200 → 60 (spike gone)
min / max	smallest / largest	10 / 200

Laplacian sharpening (2nd derivative)

∇²f = f(x+1,y) + f(x−1,y) + f(x,y+1) + f(x,y−1) − 4f(x,y)

10	10	10
10	50	10
10	10	10

0	1	0
1	-4	1
0	1	0

mask (centre −4)

∇²f = 10 + 10 + 10 + 10 − 4×50 = -160. Centre negative, so g = f − ∇²f = 50 + 160 = 210: the bright dot gets brighter, detail stands out. One-pass mask: [0 −1 0; −1 5 −1; 0 −1 0].

Sobel gradient (1st derivative)

10	10	10
10	10	10
90	90	90

-1	0	1
-2	0	2
-1	0	1

-1	-2	-1
0	0	0
1	2	1

Gx = (10 + 20 + 90) − (10 + 20 + 90) = 0. Gy = (90 + 180 + 90) − (10 + 20 + 10) = 320. |∇f| ≈ |Gx| + |Gy| = 320: a strong horizontal edge. Direction α = tan⁻¹(Gy / Gx).

Unsharp masking: mask = f − blurred f; g = f + k · mask. k = 1 unsharp, k > 1 high-boost.

1st derivative (gradient)	2nd derivative (Laplacian)
thick edges, non-zero along ramps	thin double edges, zero on ramps, zero crossing at the edge
less noise-sensitive	very noise-sensitive, strong on isolated points
gives direction	no direction, one mask

Formulas 5 · edges and segmentation

decks 08–09

Canny: 3 criteria, 5 steps

Criteria: low error rate (find real edges only), good localisation (on the true edge), single response (one pixel per edge).

Smooth with a Gaussian.
Gradient magnitude and angle (Sobel).
Non-maximum suppression: keep a pixel only if it beats its two neighbours along the gradient direction (thin edges).
Double threshold T_H and T_L (ratio 2:1 or 3:1): strong ≥ T_H, weak between.
Hysteresis: keep a weak pixel only if it is 8-adjacent to a strong one.

Thresholding

g(x,y) = 1 if f(x,y) > T, else 0 T_new = ½(μ₁ + μ₂)

Iterative T, values 10 20 30 200 210 220: start T₀ = mean = 115. Group above: mean 210; group at or below: mean 20. T₁ = ½(210 + 20) = 115 = T₀, so stop.

Region growing: start at a seed, add a 4- or 8-neighbour when |neighbour − the pixel it grows from| ≤ T, repeat until nothing joins. Split & merge: split a block into 4 while (max − min) > T, merge neighbours that are similar.

Line masks (sum 0, the 2s lie along the line): horizontal [−1 −1 −1; 2 2 2; −1 −1 −1], vertical [−1 2 −1; −1 2 −1; −1 2 −1], ±45° with the 2s on a diagonal.

Formulas 6 · chain code (the teacher's tricks)

deck 10

Compass: 0 = right, counting anticlockwise: 1 ↗, 2 ↑, 3 ↖, 4 ←, 5 ↙, 6 ↓, 7 ↘ (4-direction: 0 →, 1 ↑, 2 ←, 3 ↓).

CC: walk the boundary in the direction asked; write the arrow number of each move until you are back at the start.
CFD trick: from each digit to the next, count anticlockwise steps on the compass. Same arrow = 0. The last digit goes to the first.
NCFD trick: underline the 0s. Start at the longest run of 0s (the end joins the start), read to the end, wrap round. Two runs tie? Compare the digits right after them. No 0? Use the smallest digit.

Worked (slide 12 / SP24): CC = 0 0 7 7 5 6 5 5 4 3 2 2 2 1 2

CFD: 0→0 = 0 steps, 0→7 = 7 steps, 7→7 = 0, 7→5 = 6, … last 2→0 = 6. CFD = 070617077700716

0s at places 1, 3, 7, 11, 12. Longest run = places 11–12 (two 0s). Start there: 0 0 7 1 6 | 0 7 0 6 1 7 0 7 7 7 → NCFD = 007160706170777

what	invariant to
CC	translation
smallest shift of CC	+ start point
CFD	+ rotation (45° steps)
NCFD = shape number	start point + rotation

Formulas 7 · morphology and hit-or-miss

decks 11–12

operation	equation	plain rule	effect
erosion	A ⊖ B = {z \| (B)_z ⊆ A}	SE must fit (all 1s on object)	shrink, delete specks, split joins
dilation	A ⊕ B = {z \| (B̂)_z ∩ A ≠ ∅}	SE must hit (any 1 on object)	grow, fill holes, join gaps
opening	A ∘ B = (A ⊖ B) ⊕ B	erode, then dilate	remove small objects and thin bridges, size kept
closing	A • B = (A ⊕ B) ⊖ B	dilate, then erode	fill small holes and gaps, size kept
boundary	β(A) = A − (A ⊖ B)	object minus its eroded self	1-pixel inner outline
hit-or-miss	A ⊛ B = (A ⊖ B₁) ∩ (Aᶜ ⊖ B₂)	1s match object AND 0s match background; × ignored	corners, end points, patterns
thinning / thickening	A − (A ⊛ B) / A ∪ (A ⊛ B)	subtract / add the matches	skeleton / grow outline

1-D worked, row 1 0 0 0 1 1 1 0 1 1, SE [1 1 1] (ends ignored):

Erosion takes the minimum under the SE: windows 100, 000, 001, 011, 111, 110, 101, 011 → 0 0 0 0 1 0 0 0.

Dilation takes the maximum: → 1 0 1 1 1 1 1 1 (only the 000 window stays 0).

Memory hook: Erosion Eats, Dilation Deposits. Opening = E then D (opens gaps between things, removes specks). Closing = D then E (closes holes).

TrapShow the middle image (A ⊖ B or A ⊕ B) in every opening / closing answer. For hit-or-miss draw each SE with 1 / 0 / ×, one output grid per SE, then the OR.

Formulas 8 · compression

deck 13 · biggest marks block

what	formula	worked line
compression ratio	C_R = n₁ / n₂ (original / compressed)	512×512×8 = 2,097,152 bits; 64 KB = 524,288 bits → C_R = 4
relative redundancy	R_D = 1 − 1/C_R	1 − 1/4 = 0.75 → 75% redundant
average length	L_avg = Σ l(r_k) p(r_k)	Huffman below: 1.9 bits/symbol
entropy	H = −Σ p log₂ p	0.4·1.322 + 0.3·1.737 + 0.2·2.322 + 0.1·3.322 = 1.8464
efficiency	η = H / L_avg	1.8464 / 1.9 = 97.2%
RMSE	e_rms = √[ (1/MN) Σ (f̂ − f)² ]	every pixel +2: √(36/9) = 2
SNR (ms)	Σ f̂² / Σ (f̂ − f)²	248 / 36 = 6.889

Huffman (SP25: A 0.4, B 0.3, C 0.2, D 0.1)

Reduce: sort, merge the two smallest: C + D = 0.3 → list 0.4, 0.3, 0.3 (the sum goes below the equal value) → merge 0.3 + 0.3 = 0.6 → list 0.6, 0.4.

Code back: upper branch 0, lower 1: 0.6 = 0, 0.4 = 1 → A = 1; B = 00, (CD) = 01 → C = 010, D = 011.

L_avg = 0.4·1 + 0.3·2 + 0.2·3 + 0.1·3 = 1.9 ≥ H = 1.8464. Fixed 2-bit code → C_R = 2 / 1.9 = 1.053.

Golomb G_m(n)

q = ⌊n/m⌋ → q ones + 0 | r = n mod m, k = ⌈log₂m⌉, c = 2^k − m: r < c → r in k−1 bits, else r + c in k bits

G₄(9): q = 2 → 110; r = 1, k = 2, c = 0 → r ≥ c → 1 + 0 = 1 in 2 bits = 01 → 11001.

G₅(12): q = 2 → 110; r = 2, k = 3, c = 3 → r < c → 2 in 2 bits = 10 → 11010.

Arithmetic (slide 53: a1 0.2, a2 0.2, a3 0.4, a4 0.2; message a1 a2 a3 a3 a4)

new low = low + range × (slice start) new high = low + range × (slice end)

symbol	range before	low	high
a1	1	0	0.2
a2	0.2	0.04	0.08
a3	0.04	0.056	0.072
a3	0.016	0.0624	0.0688
a4	0.0064	0.06752	0.0688

Any number in [0.06752, 0.0688) codes the message: the slide picks 0.068.

LZW (slide 77: 4×4 image, every row 39 39 126 126)

Dictionary starts with 0–255. Read a pixel: if (current + pixel) is in the dictionary, keep extending; if not, output the code of current, add (current + pixel) at the next location (256, 257, …), restart from the pixel.

recognized	pixel	output	location	entry
	39
39	39	39	256	39-39
39	126	39	257	39-126
126	126	126	258	126-126
126	39	126	259	126-39
39	39
39-39	126	256	260	39-39-126
126	126

Full output: 39 39 126 126 256 258 260 259 257 126 → 10 codes × 9 bits = 90 bits vs 128 → C_R = 1.42.

RLE: write (value, run length). Row 10 10 10 10 12 12 → (10, 4)(12, 2). Short runs make the file bigger (C_R < 1): say so.

Which redundancy each method removes

redundancy	what it is	removed by
coding	codes longer than needed	Huffman, Golomb, arithmetic
spatial / inter-pixel	neighbours repeat or predict each other	LZW, RLE, predictive coding
irrelevant (psychovisual)	detail the eye ignores	quantization (lossy)
temporal	frames in a video repeat	frame differencing

Formulas 9 · colour

deck 14

what	formula / fact
RGB → CMY	C = 1 − R, M = 1 − G, Y = 1 − B (normalise to 0–1 first)
θ	cos⁻¹ { ½[(R − G) + (R − B)] / √[(R − G)² + (R − B)(G − B)] }
H	θ if B ≤ G, else 360° − θ (red 0°, green 120°, blue 240°)
S	1 − 3·min(R, G, B) / (R + G + B)
I	(R + G + B) / 3
24-bit colours	2²⁴ = 16,777,216

Worked (R, G, B) = (0.8, 0.4, 0.2): numerator ½(0.4 + 0.6) = 0.5; denominator √(0.16 + 0.6 × 0.2) = √0.28 = 0.5292; θ = cos⁻¹(0.9449) = 19.1°. B ≤ G, so H = 19.1°. S = 1 − 3 × 0.2 / 1.4 = 0.5714. I = 1.4 / 3 = 0.4667.

Additive (light, RGB): R + G + B = white. Subtractive (pigment, CMY): C + M + Y = black (K added because CMY black is muddy).
RGB cube: black at the origin, white at the far corner, grays on the diagonal R = G = B.
HSI separates colour (H, S) from brightness (I): good for segmentation and for enhancing I without changing hues.

Q1 theory: question → what to write

5 marks each · any 5 of 6

In plain wordsEach Q1 answer is a definition, a formula or sketch, and three short points. Below are the questions she repeats, with the points to write.

if asked	write
sampling vs quantization; why more levels look finer	coordinates vs amplitude; few pixels → blocky, few levels → false contours; bits = M·N·k
4-, 8-, m-connectivity; distance properties	the three adjacency rules; m removes double paths; D ≥ 0, symmetric, triangle inequality
image enhancement; spatial vs frequency domain	make an image more useful for a task; spatial works on pixels directly (point, neighbourhood), frequency on the Fourier transform
piecewise linear: identity, threshold, stretch	the 3-piece formula with (r₁,s₁),(r₂,s₂) and the 3 settings, each with a graph
histogram; 4 types; can you rebuild the image?	h(r_k) = n_k; dark / bright / low / high contrast sketches; no, it holds no positions
why is the equalized histogram not flat?	discrete levels: several r map to one s, some s stay empty
smoothing vs sharpening	averaging (integration) blurs, removes noise; derivatives (differentiation) bring out edges
1st vs 2nd derivative	thick vs thin double edge; ramp non-zero vs zero; 2nd strong on points, noise-sensitive
edge detection steps; Canny	smooth → gradient → threshold; Canny's 3 criteria and 5 steps
segmentation approaches	discontinuity (points, lines, edges) and similarity (threshold, region growing, split & merge)
structuring element; erosion vs dilation	small shape with an origin; fit vs hit; shrink vs grow; one application each
opening vs closing	equations, order of operations, specks vs holes, idempotent
chain code; why CFD and NCFD	boundary as direction numbers; CFD removes rotation, smallest shift removes start point
data vs information; three redundancies	data = what is stored, information = what it tells; coding, spatial, irrelevant (+ temporal)
lossless vs lossy	exact rebuild (Huffman, LZW, RLE) vs some loss for higher C_R (quantization); judge lossy with RMSE
why is Huffman optimal / entropy	shortest codes for most likely symbols, prefix-free; H is the lower bound on L_avg
additive vs subtractive; which model for printing, display, segmentation	light vs pigment; CMYK, RGB, HSI
RGB cube; how gray is formed	axes R, G, B 0–1; black origin, white (1,1,1); gray on the diagonal

Last-hour traps

read this on the bus

Find L from the bits first: 3-bit → 0…7. Using 255 on a 3-bit image ruins every number after it.
Round .5 up (3.5 → 4). HE: s = round(7 × CDF), not floor.
Median: sort all nine values, take the 5th. Zero padding at corners means five 0s.
Laplacian sign: centre negative → g = f − ∇²f; centre positive → g = f + ∇²f.
Gradient: |Gx| + |Gy|, take absolute values before adding.
Erosion = fit, dilation = hit. Opening = erode first. Closing = dilate first.
Non-symmetric SE: dilation uses the reflected SE B̂. Mark the origin.
Chain code: walk the direction the question says. The CFD's last digit wraps to the first code.
C_R = original / compressed. 1 KB = 1024 bytes = 8192 bits.
Huffman: sum goes below an equal value; upper 0, lower 1; show the full reduction table.
LZW: output the last recognized sequence at the end; count codes × 9 bits.
Golomb: unary = q ones then a 0.
HSI: normalise to 0–1 first; H = 360° − θ when B > G.
Q3: name the method in bold in the first line; give one limitation.

Practise each method step by step

deck pages with simulators

Every formula above has a full lesson page with past questions solved and a step-by-step simulator:

Decks 01–02 · fundamentals · 03 · pixels · 04 · intensity · 05 · histogram
06 · smoothing · 07 · sharpening · 08 · edges · 09 · regions
10 · chain code · 11 · morphology I · 12 · hit-or-miss · 13 · compression · 14 · colour
Trainers: chain code · LZW