Points and Pointillism

Transcription

1 Points Pointillism A Computational Perspective Partha Bhowmick Associate Professor CSE Department IIT Kharagpur

2 Points Pointillism Corners Minutiae PSPM Corners as Points

3 Points Pointillism Corners Minutiae PSPM Corners as Points

4 Points Pointillism Corners Minutiae PSPM Corners as Points

5 Points Pointillism Corners Minutiae PSPM Corners as Points

6 Points Pointillism Corners Minutiae PSPM Corners as Points Applications 1 shape analysis 2 tracking and classification of moving vehicles 3 optical flow computation 4 3D scene analysis and reconstruction from stereo image pairs 5 face tracking and face recognition 6 retrieval of images and videos etc.

7 Points Pointillism Corners Minutiae PSPM Corners as Points Shape Analysis

8 Points Pointillism Corners Minutiae PSPM Minutiae as Points

9 Points Pointillism Corners Minutiae PSPM Minutiae as Points

10 Points Pointillism Corners Minutiae PSPM Minutiae as Points

11 Points Pointillism Corners Minutiae PSPM Minutiae as Points

12 Points Pointillism Corners Minutiae PSPM Point Set Pattern Matching Object corners

13 Points Pointillism Corners Minutiae PSPM Point Set Pattern Matching Point set

14 Points Pointillism Corners Minutiae PSPM Point Set Pattern Matching Q: Does the blue point set match the black one? What s the transformation?

15 Points Pointillism Corners Minutiae PSPM Point Set Pattern Matching Treat them separately in proper local coordinate system.

16 Points Pointillism Corners Minutiae PSPM Point Set Pattern Matching Consider the longest vectors (red lines).

17 Points Pointillism Corners Minutiae PSPM Point Set Pattern Matching y x y x Define the local coordinate systems and compare the recomputed point coordinates.

18 Points Pointillism Corners Minutiae PSPM Point Set Pattern Matching y x y x Report the match.

19 Points Pointillism Corners Minutiae PSPM Point Set Pattern Matching Redraw the objects if needed.

20 Pointillism Our algorithmic artwork (in progress)

21 Unordered Point Set Object corners Too few to reconstruct

22 Unordered Point Set Sufficient?

23 Unordered Point Set Sufficient???

24 Unordered Point Set Yes, sufficient! (Pointillist factor φ = 1)

25 Unordered Point Set More than sufficient (Pointillist factor φ = 2)

26 Unordered Point Set Reconstruction

27 The idea Points Pointillism Ensemble Use the nearest neighbor (NN) rule. NN mimics our psycho-visual mechanism. Pick an optimal or suboptimal set of points so that reconstruction is possible.

28 Edge processing Procedure Find the minimum distance between two edges e i and e j of (same or different) polygon(s).

29 Edge processing Case 1 q i+1 p j p j+1 p i+1 q j q j+1 q i Lj p i

30 Edge processing Case 2 p j+1 L j p j q i q i+1 p i+1 q j qj+1 p i

31 Edge processing Case 3 p i+1 p j q i q j p i p j+1

32 Edge processing Case 4 q i+1 p i+1 q i p i q j p j q j+1 p j+1 L i L j

33 Reconstruction idea Facts about Delaunay triangulation DT (S) of any point set S: Each pair of nearest neighbors in S are neighbors in DT (S). For the Euclidean graph 1 EG(S) of S, the minimum spanning tree M ST (EG(S)) is a subgraph of DT (S). 1 If S consists of m points, then the vertices of EG(S) are the points in S and the edges are all ( n 2) undirected pairs of distinct points, the weight of each edge being given by the Euclidean distance between the corresponding points.

34 Reconstruction idea Facts about Delaunay triangulation DT (S) of any point set S: Each pair of nearest neighbors in S are neighbors in DT (S). For the Euclidean graph 1 EG(S) of S, the minimum spanning tree M ST (EG(S)) is a subgraph of DT (S). 1 If S consists of m points, then the vertices of EG(S) are the points in S and the edges are all ( n 2) undirected pairs of distinct points, the weight of each edge being given by the Euclidean distance between the corresponding points.

35 Reconstruction by Voronoi diagram Voronoi diagrams for different point sets

36 Reconstruction by Voronoi diagram Original contour C

37 Reconstruction by Voronoi diagram Pointillist ensemble Ĉ

38 Reconstruction by Voronoi diagram Voronoi diagram, V or(ĉ)

39 Reconstruction by Voronoi diagram Delaunay triangulation (in red), DT (Ĉ), from V or(ĉ)

40 Reconstruction by Voronoi diagram DT (Ĉ) = subgraph of Euclidean graph EG(Ĉ)

41 Reconstruction by Voronoi diagram Reconstructed curve (in green) = MST (DT (Ĉ))

42 Reconstruction by Voronoi diagram Original Reconstruction

43 Reconstruction by Voronoi diagram

44 Reconstruction by Voronoi diagram

45 Reconstruction by Voronoi diagram reconstructed original

46 And so is Science playing the Art...