Low-Rank Based Algorithms for Rectification, Repetition Detection and De-Noising in Urban Images. A dissertation proposal by Juan Liu

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1 Low-Rank Based Algorithms for Rectification, Repetition Detection and De-Noising in Urban Images A dissertation proposal by Juan Liu

2 Committee Committee: Professor Ioannis Stamos, Mentor, Hunter College Professor Yingli Tian, City College Professor Zhigang Zhu, City College Outside Member: Professor Emmanouil Z. Psarakis, University of Patras, Greece

3 Current Work 2D image rectification Façade texture selection Efficient Kronecker Product model Automatic repeated patterns detection Reconstruction & photorealistic rendering of urban environments, symmetry detection, hole filling, etc.

4 Façade Image Rectification Vanishing points (VPs) detection TILT Vanishing points Draw m hypothetical lines at angular intervals for each vanishing point Output

5 Façade Texture Selection Let C be the non-negative m m matrix, with each element representing the number of Harris corners inside a block Slide a window of size r c along C Compute the sample mean deviation of the sample median of matrix C, μ C

6 Façade Texture Selection

7 Kronecker Product Model

8 A Toy Example Input facade Repeated patterns

9 Repeated Patterns Detection via Kronecker Product Model Define the cost function: The minimization problem:

10 Solution to The Minimization Problem Theorem 1: Let be the Singular Value Decomposition of the rearranged counterpart of matrix. Then partition matrices, patterns and weighting factors should satisfy the following:

11 Solution to The Minimization Problem Lemma 1: Assuming that matrices are known, then the optimal and are related as follows:

Partition 3 10 partition blocks Fi,j Column-wise Cross-Correlation

12 Spatial Periods Estimation via Cross Correlation Consider that are known, then we can estimate the periods for facade partition Partition 3 10 partition blocks Fi,j Column-wise Cross-Correlation sequences: distance between the adjacent peaks provides the period information.

13 Block Vectorization Vectorization of partition blocks Vectorization The equivalent cost function: rank = 30

14 Estimating K by Clustering rank = 4 Reshape

15 Estimation of M κ, κ =1, 2,, K Reshape the K indicators vectors from Algorithm 2

16 Computing Patterns and Weighting Factors Using Lemma 1 and Algorithm 2 Group 1 Classification Refinement Group 2 Classification Refinement Group 3 Classification Refinement 1-0 patterns re-construction via Kronecker Product Model Group 4 Classification Refinement

detection 89 façade images with ground-truth Success rate 96%

17 Experiments and Evaluation Experiment 1: image rectification and texture selection Experiment 2: repeated patterns detection 89 façade images with ground-truth Success rate 96% Pixel-wise comparison Success threshold: 91% match with ground-truth

18 Results

19 Proposed Work Improve the estimation of K Extend the method to model nested patterns Apply the model to 3D point clouds

20 Improve the estimation of K Limitation: the accuracy and efficiency is drawn back by K-means clustering algorithm

21 Period Computation for Nested Patterns The current model may cut a bigger pattern into pieces due to that: The most frequently appeared pattern dominates the final period

22 Apply the model to 3D point clouds

23 Timeline My work plan to complete the dissertation is arranged as follows: Jan Jan : Finalize the implementation of new methods. Run experiments to test the new methods. Analyze the performance based upon experiment results. Jan Feb : Complete the rest part of my thesis and prepare for defense. Finally: Defend in March 2015.

24 Related Publications One paper Automatic Kronecker product model based detection of repeated patterns in 2D urban images that is related to this proposal has been published in IEEE International Conference on Computer Vision (ICCV) 2013 (accepatance rate 28%, 1600 submissions). Another related paper has been submitted to the IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) recently.

Data Acquisition, Leica Scan Station 2, Park Avenue and 70 th Street, NY

Data Acquisition, Leica Scan Station 2, Park Avenue and 70 th Street, NY Automated registration of 3D-range with 2D-color images: an overview 44 th Annual Conference on Information Sciences and Systems Invited Session: 3D Data Acquisition and Analysis March 19 th 2010 Ioannis