Every key formula from the course, one table per lecture. Click a heading to open the full lecture.
| Topic | Formula | Meaning |
|---|
| Retinal image size | $h = 17\,\text{mm}\cdot H/D$ | H = object height, D = distance (15 m tree at 100 m gives 2.55 mm) |
| Pinhole projection | $x = fX/Z,\; y = fY/Z$ | f = focal length, Z = depth |
| Thin lens | $\tfrac1f=\tfrac1u+\tfrac1v$ | u = object distance, v = image distance |
| Number of colours | $2^{\text{bpp}}$ | 24 bpp gives 16,777,216 colours |
| Image storage | $M\times N\times \text{bpp}$ bits | M rows, N columns |
| Contrast | $C=I_{max}-I_{min}$ | Spread of intensities |
| Pixel density | $\text{PPI}=\sqrt{w^2+h^2}/d$ | w, h in pixels; d = diagonal in inches |
| RGB to CMY | $[C,M,Y]^T=[1,1,1]^T-[R,G,B]^T$ | Values normalised to [0,1] |
| RGB to HSI: I and S | $I=\tfrac{R+G+B}{3},\; S=1-\tfrac{\min(R,G,B)}{I}$ | I = mean intensity; S = purity |
| RGB to HSI: hue | $\theta=\cos^{-1}\frac{\frac12[(R-G)+(R-B)]}{[(R-G)^2+(R-B)(G-B)]^{1/2}}$; $H=\theta$ if $G\ge B$, else $360^\circ-\theta$ | Hue angle: R = 0°, G = 120°, B = 240° |
| HSI to RGB (0–120°) | $B=I(1-S),\; R=I\left[1+\tfrac{S\cos H}{\cos(60^\circ-H)}\right],\; G=3I-(R+B)$ | Other sectors: subtract 120°/240° and rotate roles |
| RGB to YUV | $Y=0.299R+0.587G+0.114B,\; U=0.492(B-Y),\; V=0.877(R-Y)$ | Y = luma; U, V = colour differences |
| Topic | Formula | Meaning |
|---|
| Image negative | $s=L-1-r$ | L levels (256 for 8-bit) |
| Log transform | $s=c\log(1+r)$ | Expands dark values, compresses bright |
| Gamma (power law) | $s=c\,r^{\gamma}$ | γ < 1 brightens, γ > 1 darkens |
| Contrast stretching | $s=\frac{r-r_{min}}{r_{max}-r_{min}}(L-1)$ | Maps (r_min, r_max) to (0, L−1) |
| Normalised histogram | $p_r(r_k)=n_k/MN$ | n_k pixels at level k |
| Histogram equalisation | $s_k=(L-1)\sum_{j=0}^{k}p_r(r_j)$ | Scaled CDF, round, remap |
| Correlation | $g(x,y)=\sum_s\sum_t w(s,t)f(x+s,y+t)$ | Kernel w slid over image |
| Convolution | $g(x,y)=\sum_s\sum_t w(s,t)f(x-s,y-t)$ | Correlation with kernel rotated 180° |
| Linearity | $R(f+g)=R(f)+R(g),\ R(kf)=kR(f)$ | Plus shift invariance = LSI system |
| Box (mean) filter | $w=\frac{1}{mn}\mathbf{1}$ | Removes noise, blurs edges |
| 2D Gaussian | $G(x,y)=\frac{1}{2\pi\sigma^2}e^{-(x^2+y^2)/2\sigma^2}$ | Separable; σ sets blur |
| Topic | Formula | Meaning |
|---|
| 1st difference | $\partial f/\partial x=f(x+1)-f(x)$ | Non-zero along ramps; thick edges |
| 2nd difference | $\partial^2 f/\partial x^2=f(x+1)+f(x-1)-2f(x)$ | Zero crossing at a step; double edge |
| Laplacian | $\nabla^2f=f(x{+}1,y)+f(x{-}1,y)+f(x,y{+}1)+f(x,y{-}1)-4f(x,y)$ | Mask [0 1 0; 1 −4 1; 0 1 0]; 8-neighbour centre −8 |
| Laplacian sharpening | $g=f-\nabla^2f$ (centre −), $g=f+\nabla^2f$ (centre +) | Add edge response back |
| Unsharp masking | $g=f+(f-\bar f)$ | f̄ = blurred copy |
| High-boost | $g=f+k(f-\bar f),\ k>1$ | Stronger edge emphasis |
| Gradient magnitude | $M=\sqrt{g_x^2+g_y^2}\approx|g_x|+|g_y|$ | Edge strength |
| Gradient direction | $\theta=\tan^{-1}(g_y/g_x)$ | Perpendicular to edge |
| Sobel kernels | $G_x=[-1\,0\,1;-2\,0\,2;-1\,0\,1],\ G_y=[-1\,-2\,-1;0\,0\,0;1\,2\,1]$ | Prewitt uses 1s instead of 1,2,1 |
| Roberts cross | $G_x=[1\,0;0\,-1],\ G_y=[0\,1;-1\,0]$ | 2×2 diagonal differences |
| Laplacian of Gaussian | $\nabla^2G=\frac{x^2+y^2-2\sigma^2}{2\pi\sigma^6}e^{-\frac{x^2+y^2}{2\sigma^2}}$ | Edges at zero crossings |
| Topic | Formula | Meaning |
|---|
| Gradient | $m=\sqrt{I_x^2+I_y^2},\ \theta=\tan^{-1}(I_y/I_x)$ | Edge strength and direction |
| Harris window error | $E(u,v)=\sum_W[I(x+u,y+v)-I(x,y)]^2$ | Large for every shift = corner |
| Small-motion approx | $I(x+u,y+v)\approx I+I_xu+I_yv$ | Taylor expansion used to derive M |
| Structure tensor | $M=\sum_W\begin{bmatrix}I_x^2&I_xI_y\\I_xI_y&I_y^2\end{bmatrix}$ | $E\approx[u\,v]M[u\,v]^T$ |
| Eigenvalue cases | Flat: $\lambda_1,\lambda_2\approx0$; edge: one $\gg$ other; corner: both large | How to read M |
| Harris response | $R=\det M-k(\operatorname{tr}M)^2$, $k=0.04$–$0.06$ | R < 0 edge, |R| small flat, R > 0 large corner |
| det and trace | $\det M=\lambda_1\lambda_2,\ \operatorname{tr}M=\lambda_1+\lambda_2$ | No eigen-decomposition needed |
| Hessian detector | $\det H=L_{xx}L_{yy}-L_{xy}^2$ | Second derivatives of smoothed image |
| Scale-normalised LoG | $\sigma^2(L_{xx}+L_{yy})$ | Blob detection; radius $r\approx\sqrt2\sigma$ |
| DoG | $G(k\sigma)-G(\sigma)\approx(k-1)\sigma^2\nabla^2G$ | Cheap LoG approximation |
| Suzuki–Abe border start | Outer: $f(i,j)=1,\ f(i,j-1)=0$; hole: $f(i,j)\ge1,\ f(i,j+1)=0$ | NBD += 1 on each new border |
| Topic | Formula | Meaning |
|---|
| Scale space | $L(x,y,\sigma)=G(x,y,\sigma)*I(x,y)$ | Octave doubles σ, then downsample by 2 |
| DoG pyramid | $\mathrm{DoG}_i=G_{i+1}-G_i$ | SIFT looks for extrema here |
| SIFT extrema | $8+9+9=26$ neighbours | Max/min in 3×3×3 neighbourhood |
| SIFT edge rejection | $\mathrm{tr}(H)^2/\det(H)<(r+1)^2/r$, $r=10$ | Removes edge-like keypoints |
| SIFT orientation | $m=\sqrt{L_x^2+L_y^2},\ \theta=\tan^{-1}(L_y/L_x)$ | 36-bin histogram, dominant peak |
| SIFT descriptor | $4\times4\times8=128$-D | 16×16 patch, 16 cells, 8 bins each |
| Descriptor normalisation | $D'=D/\|D\|$ | Contrast invariance |
| LBP | $\mathrm{LBP}_{P,R}=\sum_{p=0}^{P-1}s(g_p-g_c)2^p$ | s(x) = 1 if x ≥ 0; histogram of codes is the feature |
| Gabor filter | $e^{-(x'^2+\gamma^2y'^2)/2\sigma^2}\cos(2\pi x'/\lambda+\phi)$ | λ wavelength, θ orientation, σ width, γ aspect, φ phase |
| GLCM | $P(i,j)=C(i,j)/\sum C$ | Normalised gray-level pair counts for (d, θ) |
| GLCM contrast, energy | $\sum(i-j)^2P(i,j)$, $\sum P(i,j)^2$ | Local variation; uniformity |
| GLCM homogeneity, correlation | $\sum\frac{P}{1+|i-j|}$, $\sum\frac{(i-\mu_x)(j-\mu_y)P}{\sigma_x\sigma_y}$ | Pair similarity; linear dependency |
| Topic | Formula | Meaning |
|---|
| Global threshold (BINARY) | $dst=M \text{ if } src\gt T,\ \text{else } 0$ | T = fixed threshold, M = maxval (255); other types are INV, TRUNC, TOZERO, TOZERO_INV |
| TRUNC / TOZERO | $dst=T\ (\text{TRUNC}) \text{ or } src\ (\text{TOZERO}) \text{ if } src\gt T$ | TRUNC clips values above T to T; TOZERO zeroes values at or below T |
| Adaptive mean threshold | $T(x,y)=\text{Mean}_{nbhd}-C$ | Per-pixel threshold from local mean minus constant C |
| Adaptive Gaussian threshold | $T(x,y)=\text{GaussWeightedSum}_{nbhd}-C$ | Like adaptive mean, nearer pixels weigh more |
| Otsu within-class variance | $\sigma_w^2(t)=\omega_0\sigma_0^2+\omega_1\sigma_1^2$ | Choose t that minimises this |
| Otsu class stats | $\omega=\frac{n_k}{N},\ \mu=\frac{\sum i\,n_i}{n_k},\ \sigma^2=\frac{\sum (i-\mu)^2 n_i}{n_k}$ | Weight, mean, variance of each side of the split |
| Otsu between-class variance | $\sigma_b^2=\omega_0\omega_1(\mu_0-\mu_1)^2,\ \sigma_T^2=\sigma_w^2+\sigma_b^2$ | Maximising σ_b² = minimising σ_w² |
| Erosion | $A\ominus B=\{z:B_z\subseteq A\}$ | SE must fit inside; shrinks objects |
| Dilation | $A\oplus B=\{z:B_z\cap A\ne\varnothing\}$ | SE hits object; grows objects |
| Opening | $A\circ B=(A\ominus B)\oplus B$ | Erode then dilate; removes specks and spurs |
| Closing | $A\bullet B=(A\oplus B)\ominus B$ | Dilate then erode; fills holes and gaps |
| Boundary extraction | $A-(A\ominus B)$ | Object minus its erosion = outline |
| Topic | Formula | Meaning |
|---|
| Gaussian kernel | $G(x,y)=\frac{1}{2\pi\sigma^2}e^{-\frac{x^2+y^2}{2\sigma^2}}$ | Canny step 1; 3×3 version is (1/16)[1 2 1; 2 4 2; 1 2 1] |
| Sobel gradients | $G_x=I*S_x,\ G_y=I*S_y$ | S_x=[-1 0 1; -2 0 2; -1 0 1], S_y=[-1 -2 -1; 0 0 0; 1 2 1] |
| Gradient magnitude | $M=\sqrt{G_x^2+G_y^2}$ | Edge strength |
| Gradient direction | $\theta=\tan^{-1}(G_y/G_x)$ | Perpendicular to edge; rounded to 0/45/90/135° for NMS |
| Non-maximum suppression | $M(x,y)=G \text{ if } G\ge G(N_1)\text{ and }G\ge G(N_2),\ \text{else } 0$ | N1, N2 = neighbours along gradient; thins edges to 1 px |
| Canny double threshold | $M\gt T_H$ strong; $T_L\lt M\lt T_H$ weak; $M\lt T_L$ none | Hysteresis keeps weak pixels connected to strong (T_H:T_L ≈ 2:1 to 3:1) |
| Background subtraction | $F(x,y)=\lvert I_t(x,y)-B(x,y)\rvert$ | Threshold F, clean with morphology |
| Frame differencing | $D=\lvert I_t-I_{t-1}\rvert$ | Fast; misses slow objects |
| Running average background | $B_t=\alpha I_t+(1-\alpha)B_{t-1}$ | α = learning rate |
| Topic | Formula | Meaning |
|---|
| Brightness constancy | $I(x,y,t)=I(x+\Delta x,y+\Delta y,t+\Delta t)$ | Moving pixel keeps its intensity |
| Optical flow constraint | $I_xu+I_yv+I_t=0$ | One equation, two unknowns (aperture problem) |
| Normal flow | $(u,v)_\perp=-\dfrac{I_t}{\|\nabla I\|^2}\nabla I$ | Only component along gradient observable |
| Lucas–Kanade solution | $\begin{bmatrix}u\\v\end{bmatrix}=\begin{bmatrix}\sum I_x^2&\sum I_xI_y\\\sum I_xI_y&\sum I_y^2\end{bmatrix}^{-1}\begin{bmatrix}-\sum I_xI_t\\-\sum I_yI_t\end{bmatrix}$ | Same flow in window; reliable at corners |
| Horn–Schunck energy | $E=\iint (I_xu+I_yv+I_t)^2+\lambda(|\nabla u|^2+|\nabla v|^2)$ | Data + smoothness; dense flow |
| Horn–Schunck update | $u=\bar u-\dfrac{I_x(I_x\bar u+I_y\bar v+I_t)}{\lambda+I_x^2+I_y^2}$ | ū, v̄ = neighbour averages |
| Pyramid scaling | $d_L=d/2^L$ | Coarse-to-fine for large motion |
| Topic | Formula | Meaning |
|---|
| Single / complete / average link | $\min d\;/\;\max d\;/\;\frac1{|A||B|}\sum d(a,b)$ | Inter-cluster distances |
| Background update | $\mathcal B^{(n+1)}=\dfrac{w_a\mathcal F+\sum_i w_i\mathcal B^{(n-i)}}{w_c}$ | Foreground if $|\mathcal F-\mathcal B|>T$ |
| K-means objective | $J=\sum_j\sum_{x\in C_j}\|x-\mu_j\|^2$ | Assign to nearest centre, recompute means, repeat |
| Affinity | $\mathrm{aff}(x,y)=\exp\{-\|x-y\|^2/2\sigma_d^2\}$ | Gaussian similarity in [0, 1] |
| Cut | $\mathrm{Cut}(A,B)=\sum_{i\in A,j\in B}w_{ij}$ | Weight of severed edges |
| Normalised cut | $\dfrac{\mathrm{Cut}(A,B)}{\mathrm{Assoc}(A,V)}+\dfrac{\mathrm{Cut}(A,B)}{\mathrm{Assoc}(B,V)}$ | Balanced partitions |
| Spectral clustering | $(D-W)\mathbf y=\lambda D\mathbf y$ | Second-smallest eigenvector, split by sign |
| Topic | Formula | Meaning |
|---|
| Mask response | $R=\sum_{k=1}^{9}w_kz_k,\ |R|\ge T$ | Point mask: 8 centre, −1 elsewhere |
| Gradient | $\|\nabla f\|=\sqrt{G_x^2+G_y^2}\approx|G_x|+|G_y|$ | $\alpha=\tan^{-1}(G_y/G_x)$ |
| Laplacian | $\nabla^2f=f_{xx}+f_{yy}$ | Zero crossings; noise-sensitive |
| LoG (unnormalised) | $\nabla^2G=\dfrac{x^2+y^2-2\sigma^2}{\sigma^4}e^{-\frac{x^2+y^2}{2\sigma^2}}$ | Mexican hat; zero crossing at $r=\sqrt2\sigma$ |
| Thresholding | $g=1$ if $f>T$ else $0$ | T in histogram valley |
| Region conditions | $\cup R_i=R;\ R_i\cap R_j=\varnothing;\ P(R_i)=T;\ P(R_i\cup R_j)=F$ | Connected, disjoint, homogeneous |
| Homogeneity predicate | $\max(R)-\min(R)<T$ or $\sigma<T$ | FALSE → split into 4 quadrants |
| Merge rule | Merge $R_i,R_j$ if $P(R_i\cup R_j)=\text{TRUE}$ | Adjacent regions only |
| Topic | Formula | Meaning |
|---|
| Single link | $D(A,B)=\min_{x\in A,y\in B}d(x,y)$ | Closest pair; chains. Slide merge heights: 2, 6, 7, 15 |
| Complete link | $D(A,B)=\max_{x\in A,y\in B}d(x,y)$ | Farthest pair; compact. Merge heights: 2, 7, 15, 30 |
| Pixel distance | $d(i,j)=|I_i-I_j|$ | n items need n − 1 merges |
| Watershed | Minima = seeds; flood by level; pixel reached by two basins = W | Intensity is height; dams = watershed lines |
| Hough line (m-c) | $c=-x_i m+y_i$ | Point ↔ line in parameter space; fails for vertical lines |
| Hough line (ρ-θ) | $\rho=x\cos\theta+y\sin\theta$ | Bounded space; a point becomes a sinusoid |
| Accumulator update | $A(m,c)\leftarrow A(m,c)+1$ | Peaks = detected lines |
| Circle HT | $(x_i-a)^2+(y_i-b)^2=r^2$ | 2D A(a,b) for known r; 3D A(a,b,r) otherwise |
| Circle HT with gradient | $a=x_i-r\cos\phi_i,\ b=y_i-r\sin\phi_i$ | One vote per edge point |
| Generalised HT | $x_c=x_i+r_k^i\cos\alpha_k^i,\ y_c=y_i+r_k^i\sin\alpha_k^i$ | φ-table (R-table) lookup by edge direction |
| Topic | Formula | Meaning |
|---|
| Hough numerical | $\rho=x\cos\theta+y\sin\theta$, $\theta\in\{0,45,90,135\}^\circ$ | (0,1),(1,2),(2,3): 3 votes at (135°, 0.71) → y = x + 1 |
| Least squares error | $E=\sum_{i}(y_i-mx_i-b)^2=\|Y-XB\|^2$ | Vertical residuals |
| Normal equation | $B=(X^TX)^{-1}X^TY$ | $m=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum x)^2}$ |
| Total least squares | $E=\sum_i(ax_i+by_i-d)^2,\ a^2+b^2=1$ | Perpendicular distance; handles vertical lines |
| Robust estimator | $\rho(u;\sigma)=\dfrac{u^2}{\sigma^2+u^2}$ | Saturates at 1 for outliers |
| RANSAC threshold | $t^2=3.84\,\sigma^2$ | 95% of inliers inside t |
| RANSAC iterations | $N=\dfrac{\log(1-p)}{\log\!\big(1-(1-e)^s\big)}$ | p confidence, e outlier ratio, s sample size; round up |
| RANSAC minimal sets | line 2, translation 1, affine 3, homography 4, F 8 (7) | Smallest sample defining the model |
| Snake energy | $\mathcal E=\int(\alpha E_{cont}+\beta E_{curv}+\gamma E_{img})ds$ | Minimise over contour |
| Snake continuity | $E_{cont}=\|p_i-p_{i-1}\|^2$ | Keeps points close |
| Snake curvature | $E_{curv}=\|p_{i+1}-2p_i+p_{i-1}\|^2$ | Penalises bending |
| Snake image term | $E_{img}=-\|\nabla I\|$ | Pulls contour onto edges |
| Topic | Formula | Meaning |
|---|
| Depth from disparity | $Z=\dfrac{fB}{d},\ d=x_L-x_R$ | f focal length (px), B baseline; near = large d |
| 3D back-projection | $X=\frac{(x-c_x)Z}{f_x},\ Y=\frac{(y-c_y)Z}{f_y}$ | Pixel + depth to world coordinates |
| Essential matrix | $x_R^TEx_L=0,\ E=[\mathbf t]_\times R$ | Normalised coords; rank 2, 5 DOF |
| Skew matrix | $[\mathbf t]_\times=\begin{pmatrix}0&-t_z&t_y\\t_z&0&-t_x\\-t_y&t_x&0\end{pmatrix}$ | Cross product as a matrix |
| Fundamental matrix | $p_R^TFp_L=0,\ F=K_R^{-T}EK_L^{-1}$ | Pixel coords; rank 2, 7 DOF |
| Epipolar lines | $\mathbf l_R=Fp_L,\ \mathbf l_L=F^Tp_R$ | Match must lie on this line |
| Epipoles | $Fe_L=0,\ F^Te_R=0$ | Null vectors of F and Fᵀ |
| 8-point row | $[x'x,\ x'y,\ x',\ y'x,\ y'y,\ y',\ x,\ y,\ 1]\,\mathbf f=0$ | Solve Af = 0 by SVD, then force rank 2 |
| Normalised 8-point | $F=T'^TF_nT$ | Centroid 0, mean distance √2, then denormalise |
| 7-point | $F=\alpha F_1+(1-\alpha)F_2,\ \det F=0$ | Cubic in α, up to 3 solutions |
| Window matching | $SAD=\sum|I_L(x{+}u,y{+}v)-I_R(x{+}u{-}d,y{+}v)|$ | Pick d with smallest cost; SSD squares |
| Topic | Formula | Meaning |
|---|
| Euclidean distance | $d(D_1,D_2)=\sqrt{\sum_i(D_{1i}-D_{2i})^2}$ | Float descriptors (SIFT) |
| Ratio test | $r=d_1/d_2$, accept if $r\lt0.8$ | Reject ambiguous matches |
| SSD / SAD | $\sum(H-F)^2,\ \sum|H-F|$ | Lower = more similar |
| NCC | $\dfrac{\sum(H-\bar H)(F-\bar F)}{\sqrt{\sum(H-\bar H)^2}\sqrt{\sum(F-\bar F)^2}}$ | In [−1, 1], higher better; brightness-robust |
| Hamming distance | $d_H=\sum_i D_1(i)\oplus D_2(i)$ | Binary descriptors (ORB, BRIEF) |
| Rotation | $\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}$ | 1 DOF |
| Translation (homogeneous) | $\begin{bmatrix}1&0&t_x\\0&1&t_y\\0&0&1\end{bmatrix}$ | Needs homogeneous coords |
| Composition | $T=T_2T_1$ | T₁ applied first; order matters |
| Affine (6 DOF) | $\begin{bmatrix}a&b&t_x\\c&d&t_y\\0&0&1\end{bmatrix}$ | Parallel lines stay parallel; 3 point pairs |
| Homography (8 DOF) | $\mathbf x'\sim H\mathbf x,\ h_{33}=1$ | Divide by w′; needs 4 point pairs |
| Topic | Formula | Meaning |
|---|
| Euclidean distance (KNN) | $d=\sqrt{\sum_j (q_j-p_j)^2}$ | Take K nearest, majority vote |
| SVM decision rule | $f(x)=w^Tx+b,\ \hat y=\text{sign}(f(x))$ | w normal to hyperplane, b bias |
| SVM margin | $\text{margin}=\dfrac{2}{\lVert w\rVert}$ | Maximise it |
| Distance to hyperplane | $\dfrac{|w^Tx+b|}{\lVert w\rVert}$ | Point to decision boundary |
| Artificial neuron | $a=f\big(\sum_j w_jx_j+b\big)$ | Weighted sum + bias through activation |
| ReLU / sigmoid | $\max(0,x),\ \dfrac1{1+e^{-x}}$ | Ranges [0, ∞) and (0, 1) |
| Gradient descent | $w\leftarrow w-\eta\,\partial L/\partial w$ | η = learning rate |
| HMM joint probability | $P(X,S)=\pi_{s_1}B_{s_1}(x_1)\prod_{t\ge2}A_{s_{t-1}s_t}B_{s_t}(x_t)$ | π initial, A transition, B emission |
| HMM forward step | $\alpha_{t+1}(j)=\big[\sum_i\alpha_t(i)A_{ij}\big]B_j(x_{t+1})$ | Viterbi replaces sum with max |
| Conv output size | $O=\Big\lfloor\dfrac{N+2P-F}{S}\Big\rfloor+1$ | N input, F kernel, P padding, S stride |
| Conv layer parameters | $(F\cdot F\cdot C_{in}+1)\cdot K$ | K filters; pooling has 0 params |
| FC layer parameters | $n_{in}\cdot n_{out}+n_{out}$ | Weights + biases |
| Topic | Formula | Meaning |
|---|
| IoU | $\text{IoU}=\dfrac{A_I}{A_P+A_G-A_I}$ | Slide example: 16/56 ≈ 0.286 |
| Intersection box | $x_l=\max(x_1,x_1'),\ x_r=\min(x_2,x_2')$ (same for y) | $A_I=\max(0,x_r-x_l)\max(0,y_b-y_t)$ |
| Precision | $\dfrac{TP}{TP+FP}$ | Fraction of detections correct |
| Recall | $\dfrac{TP}{TP+FN}$ | Fraction of objects found |
| AP and mAP | $AP=\int P\,dR,\ \text{mAP}=\frac1C\sum_c AP_c$ | Area under PR curve, averaged over classes |
| NMS rule | Keep top score; drop boxes with $\text{IoU}>T$ | Typically T = 0.5 |
| YOLO output size | $S\times S\times(5B+C)$ | e.g. 7×7×30 |
| Detection loss | $L=L_{cls}+\lambda L_{loc}$ | Classification + localisation |