Computer and Robot Vision I

Computer and Robot Vision I Chapter 6 Neighborhood Operators Presented by: 傅楸善 & 何育哲 0937 960 615 r94922131@ntu.edu.tw 指導教授: 傅楸善博士 Digital Camera and Computer Vision Laboratory Department of Computer Science and Information Engineering National Taiwan University, Taipei, Taiwan, R.O.C.

6.1 Introduction • neighborhood operator: workhorse of low level vision • neighborhood operator: performs conditioning, labeling, grouping DC & CV Lab. CSIE NTU

6.1 Introduction • The output of a neighborhood operator at a given pixel position is a function of the position, of the input pixel value at the position, of the values of the input pixels in some neighborhood around the given input position, and possibly of some values of previously generated output pixels DC & CV Lab. CSIE NTU

6.1 Introduction • numeric domain: arithmetic operations, +, -, min, max • symbolic domain: Boolean operations, AND, OR, NOT, table-look-up • nonrecursive neighborhood operators: output is function of input • recursive neighborhood operators: output depends partly on previous output DC & CV Lab. CSIE NTU

6.1 Introduction • neighborhood might be small and asymmetric or large DC & CV Lab. CSIE NTU

6.1 Introduction • : set of neighboring pixel positions around position general nonrecursive neighborhood operator : input , output DC & CV Lab. CSIE NTU

6.1 Introduction • linear operator: one common nonrecursive neighborhood operator • output possibly: position-dependent linear combination of inputs DC & CV Lab. CSIE NTU

6.1 Introduction • shift-invariant: position invariant, action same regardless of position • composition of shift-invariant operators: shift-invariant DC & CV Lab. CSIE NTU

6.1 Introduction • cross-correlation of with • : weight function: kernel or mask of weights • : domain of DC & CV Lab. CSIE NTU

6.1 Introduction • common masks for noise cleaning, (a) box filter DC & CV Lab. CSIE NTU

6.1 Introduction • common masked for noise cleaning DC & CV Lab. CSIE NTU

6.1 Introduction • application of mask with weights to image 7.69 DC & CV Lab. CSIE NTU

6.1 Introduction • convolution of with • convolution: close relative to cross-correlation • convolution: linear shift-invariant • if mask symmetric, convolution, and correlation the same DC & CV Lab. CSIE NTU

6.2 Symbolic Neighborhood Operators • indexing of neighborhoods DC & CV Lab. CSIE NTU

6.2.1 Region-Growing Operator • : projection, outputs first or second argument • : background • background pixel labeled first nonbackground label DC & CV Lab. CSIE NTU

6.2.1 Region-Growing Operator • 4-connected • output DC & CV Lab. CSIE NTU

6.2.1 Region-Growing Operator • 8-connected • output DC & CV Lab. CSIE NTU

6.2.1 Region-Growing Operator DC & CV Lab. CSIE NTU

6.2.2 Nearest Neighbor Sets and Influence Zones • influence zones: nearest neighbor sets • influence zones: iteratively region-growing DC & CV Lab. CSIE NTU

6.2.2 Nearest Neighbor Sets and Influence Zones • 4-neighborhood for city-block distance e.g. ( i , j ), ( k , l ) | ( k – i ) | + | ( l – j ) | • 8-neighborhood for max distance (of horizontal and vertical distances) e.g. ( i , j ), ( k , l ) max( | k – i | , | l – j | ) • alternate 4, 8-neighborhood for Euclidean distance DC & CV Lab. CSIE NTU

Take a Break DC & CV Lab. CSIE NTU

6.2.3 Region-Shrinking Operator • region-shrinking: changes all border pixels to background • region-shrinking: can change connectivity • region-shrinking: can entirely delete region if repeatedly applied DC & CV Lab. CSIE NTU

6.2.3 Region-Shrinking Operator • : whether or not arguments identical • : background • border: has different neighbor and becomes background DC & CV Lab. CSIE NTU

6.2.3 Region-Shrinking Operator • 4-connected: • output: DC & CV Lab. CSIE NTU

6.2.3 Region-Shrinking Operator • 8-connected: • output: DC & CV Lab. CSIE NTU

6.2.3 Region-Shrinking Operator • region shrinking: related to binary erosion except on labeled region DC & CV Lab. CSIE NTU

6.2.3 Region-Shrinking Operator DC & CV Lab. CSIE NTU

6.2.4 Mark-Interior/Border-Pixel Operator • mark-interior/border-pixel operator marks all interior pixels with the label and all border pixels with the label DC & CV Lab. CSIE NTU

6.2.4 Mark-Interior/Border-Pixel Operator • : whether or not arguments identical • : recognizes whether or not its argument is symbol DC & CV Lab. CSIE NTU

6.2.4 Mark-Interior/Border-Pixel Operator • 4-connected: • output: DC & CV Lab. CSIE NTU

6.2.4 Mark-Interior/Border-Pixel Operator • 8-connected: • output: DC & CV Lab. CSIE NTU

6.2.5 Connectivity Number Operator • connectivity number: nonrecursive and symbolic data domain • connectivity number: classify the way pixel connected to neighbors • six values of connectivity: five for border, one for interior • border: isolated, edge, connected, branching, crossing DC & CV Lab. CSIE NTU

4-connectivity 6.2.5 Connectivity Number Operator DC & CV Lab. CSIE NTU

6.2.5 Connectivity Number Operator • corner neighborhood DC & CV Lab. CSIE NTU

6.2.5 Connectivity Number Operator DC & CV Lab. CSIE NTU

Yokoi Connectivity Number • 4-connectivity • : corner transition • : corner all , no transition • : center , neighbor , nothing will happen DC & CV Lab. CSIE NTU

Yokoi Connectivity Number • 5: no transition all 8 neighbors 1, thus interior • : 1 transition generates one connected component if center removed connectivity number DC & CV Lab. CSIE NTU

Yokoi Connectivity Number DC & CV Lab. CSIE NTU

Yokoi Connectivity Number • lena.64*64 DC & CV Lab. CSIE NTU

Yokoi Connectivity Number • lena.yokoi DC & CV Lab. CSIE NTU

Yokoi Connectivity Number • 8-connectivity, only slightly different • : center and corner transition • : corner no transition, all • : itself and two 4-neighbors , corner DC & CV Lab. CSIE NTU

Computer and Robot Vision I