Unit_3 Computer vision artificial intelligence.pdf

Unit of AI

1. UNIT-3

2. Edge detection
▶The process which involves detecting sharp edges in the image
and producing a binary image as the output.
▶Rapid change in image intensity

3. Sobel Edge filter
▶Computes approxmiation of the gradient of an image intensity
function.
▶Depends on first order derviatives.
Demerits:Not accurate results and discontinuity

4. Laplacian Filter
▶The 2D images, the derivative is taken in both dimensions.
▶Second derivative operator.
▶Detects regions of rapid intensity change.
∇
2
f(x,y) =
∂
2
f
∂x
2
+
∂
2
f
∂y
2
Note
Very sensitive to noise

5. Gaussian Blur
▶Definition:Gaussian Blur is a low-pass filter that reduces
noise and detail using a Gaussian (bell curve) function.
▶Steps:
1.
2.
3.
4.
▶Effect:Center pixels get higher weight, surrounding pixels
contribute less⇒smooth and blurred image.
Example Flow:
Image Patch
Kernel
−−−−→Multiply + Sum−→Blurred Pixel

6. Canny edge detection
Definition
A multi-stage process designed to find a wide range of edges while
being robust to noise. The algorithm produces thin, continuous
edges by following a series of steps.

7. Algorithm Overview
1.Step 1:Noise Reduction (Gaussian Blur)
2.Step 2:Gradient Calculation (via Sobel filters)
3.Step 3:Non-Maximum Suppression (edge thinning)
4.Step 4:Double Thresholding (classifying strong vs weak
edges)
5.Step 5:Edge Tracking by Hysteresis (connecting edges)

8. Canny Step 1: Noise Reduction
▶Smooth the image to avoid false edges from noise.
▶Use a Gaussian blur (low-pass filter) on the input image.
▶Heavier blur (largerσ) removes more noise but risks losing
fine edges.
▶Output: a denoised image suitable for gradient calculation.

9. Canny Step 2: Finding Intensity Gradients
▶Compute horizontal and vertical derivatives on the smoothed
image (e.g., Sobel filters) to getGx,Gy.
▶Gradient magnitude:
G=
q
G
2
x+G
2
y
▶Gradient direction (angle):
θ= atan2(Gy,Gx)
▶(Often) Quantizeθto 0
◦
,45
◦
,90
◦
,135
◦
for the next step.

10. Canny Step 3: Non-Maximum Suppression
▶Goal: thin thick/blurred edges to single-pixel width.
▶For each pixel, look along the gradient directionθ.
▶Keep the pixel only if its magnitudeGis a local maximum vs.
the two neighbors alongθ.
▶Otherwise suppress (set to zero)⇒thin, well-localized edges.

11. Canny Step 4: Double Thresholding
▶Choose two thresholds:Thigh>Tlow.
▶IfG≥Thigh⇒strong edge.
▶IfG<Tlow⇒non-edge(suppress).
▶IfTlow≤G<Thigh⇒weak edge(candidate; decided next).
▶Common practice:Thigh:Tlowratio around 2:1 or 3:1 (tune
per image).

12. Canny Step 5: Edge Tracking by Hysteresis
▶Traverse weak edges and keep only those connected
(8-connectivity) to any strong edge.
▶Discard isolated weak edges (likely noise).
▶Result: clean, continuous edge map with gaps filled and false
edges removed.

13. Laplacian of Gaussian (LoG) Edge Detection
▶Idea:Combine Gaussian smoothing (noise reduction) with
Laplacian (second derivative) for robust edge detection.
▶Steps:
1.
2.
3. zero-crossingsof the LoG output.
▶LoG Kernel:A single “Mexican Hat” shaped filter that
merges both steps.
▶Key Concept:
▶Zero Crossings⇒Edge locations.
▶Scale (σ):Smallσfinds fine edges; largeσfinds coarse edges.
Result:More reliable edges, less sensitive to noise compared to
plain Laplacian.

14. Difference of Gaussians (DoG)
▶Idea:Efficient approximation of the Laplacian of Gaussian
(LoG).
▶Steps:
1. σ:
▶Smallσ1: retains details (light blur).
▶Largeσ2: smooths details (heavy blur).
2.
▶Mathematical Formulation:
D(x,y) =
Γ
Gσ1
(x,y)∗I(x,y)
∆
−
Γ
Gσ2
(x,y)∗I(x,y)
∆
▶Effect:Acts as aband-pass filter— enhances edges and
fine details while suppressing noise and background.
Result:Fast, simple edge detector widely used in feature
extraction (e.g., SIFT).

15. Hough Transform: Definition & Motivation
▶Definition:A feature extraction technique to detect shapes
(e.g., lines) by mapping points from image space (x,y) into
parameter space (ρ, θ).
▶Why not Cartesian form?
▶Line in Cartesian:y=mx+b→fails for vertical lines
(m→ ∞).
▶Solution: Use polar representation:
ρ=xcosθ+ysinθ
▶Every line is uniquely represented by (ρ, θ).
xy(x,y)θρCurve in (ρ, θ)Transform

16. Hough Transform: Steps
1.Pre-processing with Edge Detection:
▶Input: Binary edge map (e.g., from Canny detector).
▶Reduces data to only potential edge pixels.
2.Creating the Accumulator Array:
▶Define 2D array indexed by quantizedρ(rows) andθ
(columns).
▶Initialize all cells to zero.
▶Array resolution controls precision of detected lines.

17. Hough Transform: Steps
3.Voting on Parameters:
▶For each edge pixel (x,y), loop overθ.
▶Computeρ=xcosθ+ysinθ.
▶Increment accumulator at (ρ, θ).
4.Finding Peaks:
▶Identify accumulator cells with highest votes.
▶Peaks correspond to strongest candidate lines.
5.Extracting Lines:
▶Apply threshold to keep significant peaks.
▶Map (ρ, θ) back to original image to draw lines.

18. Algorithm 1Hough Voting
1:procedureHough Voting(X,Θ)
2:X: data Θ: Quantized parameterθmin, . . . , θmax
3:A: accumulator array, initially zero
4:for(x,y)∈Xdo
5: forθ∈Θdo
6: ρ=xcosθ+ysinθ
7: ▷for each set of model parameters consistent with
a sample, incrementA
8: A[θ, ρ] =A[θ, ρ] + 1
9: end for
10:end for
11:Non-maximum Suppression: detect local maxima inA
12:end procedure

19. Harris Corner Detector
The Harris corner detector identifies corners by examining a small
patch around each pixel and checking if intensity changes in all
directions.
Harris Corner Detector Steps
1.Calculate Gradients:ComputeIx,Iy(e.g., Sobel operator).
These measure rate of intensity change.
2.Form Harris Matrix (Structure Tensor):
M=
X
x,y
w(x,y)
ˇ
I
2
xIxIy
IxIyI
2
y
˘
wherew(x,y) is a weighting function (often Gaussian).

20. Harris Corner Detector Steps
3.Compute Corner Response:
R= det(M)−k·(trace(M))
2
=λ1λ2−k·(λ1+λ2)
2
Ris large and positive at corners.k∈[0.04,0.06].
4.Thresholding & Non-Maximum Suppression:Apply
threshold toRto select strong responses, then use
non-maximum suppression to keep only local maxima as
corners.

21. Hessian-Affine Detector
▶Definition:Local invariant feature detector based on the
Hessian matrix of second-order image derivatives.
H(x,y) =
ˇ
IxxIxy
IxyIyy
˘
,det(H) =IxxIyy−I
2
xy
▶The basic ideas of detecting corners remain the same as the
Harris detector, the Hessian detector makes use of the Hessian
matrix and determinant, instead of second-moment matrix M
and corner response function R

22. Hessian-Affine Detector (Process Flow)
Input ImageCompute Gaussian DerivativesForm Hessian MatrixCompute Determinant of HessianFind Local Maxima across ScalesAffine Normalization (Elliptical→Circular)Detected Keypoints

23. Gabor Filter
▶Definition:Linear filter combining a Gaussian envelope with
a sinusoidal wave.
g(x,y) = exp
`
−
x
′2
+γ
2
y
′2
2σ
2
´
cos
`
2π
x
′
λ
+ψ
´
▶Parameters:Wavelength (λ), Orientation (θ), Phase (ψ),
Spread (σ), Aspect ratio (γ).
▶Idea:Acts as a band-pass filter sensitive to edges and
textures at specific orientations and frequencies.

24. Gabor Filter (Process Flow)
Input ImageDefine Gabor Kernel (λ, θ, σ, γ)Convolve Image with KernelRepeat for Multi-Scale and Multi-OrientationFiltered Feature Maps

25. Discrete Wavelet Transform
▶Definition:Multi-resolution image analysis using low-pass
(approximation) and high-pass (detail) filters.
▶2D Decomposition:
▶LL = Approximation (low frequency both directions)
▶LH = Horizontal details
▶HL = Vertical details
▶HH = Diagonal details
▶Applications:Image compression (JPEG2000), denoising,
texture classification.

26. DWT (Process Flow)
Input ImageApply 1D DWT on RowsApply 1D DWT on ColumnsObtain Sub-bands (LL, LH, HL, HH)Recursive Decomposition on LL (Multi-level)

27. Contour-based Segmentation: Definition
Definition:Contour-based segmentation separates an image into
regions by identifying and representing theirboundaries or
contours.
▶Finds closed curves separating foreground and background.
▶Effective when objects have sharp boundaries.
▶Used in shape recognition and measurement.

28. Contour-based Segmentation: Process (Flowchart)
Input ImagePreprocessing (Noise reduction, Grayscale)Edge Detection (Canny, Sobel)Contour Tracing (Connected Curves)Contour Representation (Chain code, Polygon, Snakes)Segmented Regions

29. Contour-based Segmentation: Applications
Applications:
▶Medical Imaging:Organ and tumor detection.
▶Object Tracking:Detecting moving objects in video.
▶Robotics:Object recognition and manipulation.
▶Quality Control:Shape-based product inspection.

30. Region-based Segmentation: Definition
Definition:Partitions an image intohomogeneous connected
regionsby grouping adjacent pixels with similar properties.
▶Directly identifies regions instead of boundaries.
▶Suitable when objects have uniform intensity or color.

31. Region-Based Segmentation Techniques
Region Growing (Bottom-Up)
▶Seed Selection:Start with one or more seed pixels inside
object of interest.
▶Growing:Iteratively add neighbors satisfying similarity
criterion (e.g., intensity range).
▶Stopping Condition:Stop when no more pixels can be
added.
Region Splitting (Top-Down)
▶Initialization:Treat entire image as one large region.
▶Splitting:Non-homogeneous regions are split into smaller
sub-regions.
▶Recursive Splitting:Continue until all regions are
homogeneous.

32. Region-Based Segmentation Techniques
Region Splitting & Merging (Hybrid)
▶Image is first split into regions (e.g., using quadtree).
▶Adjacent similar regions are merged.
▶Reduces over-segmentation compared to pure splitting.

33. Region-based Segmentation: Applications
Applications:
▶Medical Imaging:Tumor or organ segmentation.
▶Satellite Imagery:Land classification (water, forest, etc.).
▶Object Recognition:Isolating colored/textured objects.

34. Level Set Representation: Definition
Definition:Represents object boundaries implicitly as the
zero-level setof a functionϕ(x,y).
▶ϕ(x,y) = 0→Boundary.
▶ϕ(x,y)<0→Inside object.
▶ϕ(x,y)>0→Outside object.

35. Level Set Representation: Process (Flowchart)
Initializeϕ(x,y) (Signed Distance)Evolution using PDEsInternal Force(Smoothness, Curvature)External Force(Edges, Intensity)Update Level SetFinal Segmentation

36. Level Set Method: Steps
Process 1: Initialize Level Set Function
▶Give an Image data
▶Convert image domain into aSigned Distance Function
(SDF).
▶Definesϕ(x,y) with:
▶ϕ <0: inside the contour
▶ϕ >0: outside the contour
▶ϕ= 0: at the contour
Process 2: Evolution by PDE
▶Updateϕ(x,y) iteratively using PDE.
▶Forces:
▶Internal Force:smoothens contour (curvature).
▶External Force:attracts contour to object edges
(gradients/statistics).

37. Level Set Representation: Applications
Process 3: Segmentation Result
▶Iteration continues until contour stabilizes.
▶Output→Object boundary (segmented image).
Applications:
▶Medical Imaging:Heart ventricles, blood vessels.
▶Fluid Dynamics:Tracking fluid boundaries.
▶Object Tracking:Deforming or splitting objects.

38. Fourier Descriptors
Concept:Represent a shape’s boundary using the Discrete Fourier
Transform (DFT).
▶Shape boundary→1D signal of complex numbers:
▶Real part: x-coordinate
▶Imaginary part: y-coordinate
▶Apply DFT⇒transform from spatial domain to frequency
domain.
▶Fourier Descriptors:The complex coefficients obtained from
DFT.
Properties:
▶Low frequencies⇒Coarse/global shape.
▶High frequencies⇒Fine details/sharp corners.
▶Invariant to translation, scaling, and rotation.
▶Useful for shape recognition and matching.

39. Wavelet Descriptors
Concept:Represent a shape’s contour using Wavelet Transform.
▶Shape boundary→1D signal.
▶Apply Wavelet Transform⇒decomposes into scales and
positions.
▶Wavelet coefficients = Wavelet Descriptors.
Advantages:
▶Localized in both space and frequency.
▶Captures sharp corners/abrupt changes without altering entire
descriptor.
▶Providesmulti-resolutionrepresentation of shape.
▶More robust to local irregularities compared to Fourier
descriptors.

40. Multi-resolution Analysis (MRA)
Foundation of Wavelet Transform:Analyze signals at multiple
levels of detail.
▶Uses two functions:
▶Scaling Function:Low-pass filter, captures coarse
(low-frequency) info.
▶Wavelet Function:Band-pass filter, captures fine
(high-frequency) details.
▶Process:
▶Signal→Approximation + Detail.
▶Approximation is further decomposed recursively.
▶Forms a hierarchy of resolutions.
▶Enables perfect reconstruction from multi-resolution
components.
Connection:Wavelet descriptors are coefficients obtained via
MRA.

41. Comparison and Wrap-up
Fourier Descriptors:
▶Compact global representation of shape.
▶Excellent invariance (translation, scaling, rotation).
▶Sensitive to local boundary variations.
Wavelet Descriptors:
▶Multi-resolution, localized representation.
▶Captures both global shape and fine local irregularities.
▶More robust to local noise/abrupt changes.
Conclusion:Fourier→Best for global shape recognition.
Wavelets→Best for detailed/local analysis with multi-resolution.