1. On Detection of Multiple Object Instances using Hough Transforms Olga Barinova Moscow State University Victor Lempitsky University of Oxford Pushmeet Kohli Microsoft Research Cambridge

2. On Detection of Multiple Object Instances Using Hough Transforms Hough transforms oObject detection → peaks identification in Hough images oBeyond lines!!!  Ballard 1983 – Other primitives  Lowe, ICCV 1999 – Object detection  Leibe, Schiele BMVC 2003 – Object class detection  Last CVPR: Maji& Malik, Gall& Lempitsky, Gu et al. …

3. On Detection of Multiple Object Instances Using Hough Transforms Example from Gall & Lempitsky CVPR 2009 Category-level object detection

4. On Detection of Multiple Object Instances Using Hough Transforms Category-level object detection ?

5. On Detection of Multiple Object Instances Using Hough Transforms Multiple lines detection oIdentifying the peaks in Hough images is highly nontrivial in case of multiple close objects oPostprocessing (e.g. non-maximum suppression) is usually used oOur framework is similar to Hough Transforms but doesn’t require finding local maxima and suppresses non-maxima automatically

6. On Detection of Multiple Object Instances Using Hough Transforms Our framework Hough space Elements space Voting elements Hypotheses

7. On Detection of Multiple Object Instances Using Hough Transforms Our framework 1 2 3 y – labelling of hypotheses, binary variables: 1 = object is present, 0 = otherwise Hough space Elements space x – labelling of voting elements, xi = index of hypothesis, if element votes for hypothesis, xi = 0, if element votes for background

8. On Detection of Multiple Object Instances Using Hough Transforms Our framework 1 2 3 x – labelling of voting elements, xi = index of hypothesis, if element votes for hypothesis, xi = 0, if element votes for background x 2 =1 x 3 =1 x 4 =2 x 5 =2 x 6 =2 x 7 =0 x 8 =2 x 1 =1 y 1 =1 y 2 =1 y 3 =0 Key idea : joint MAP-inference in x and y Hough space Elements space y – labelling of hypotheses, binary variables: 1 = object is present, 0 = otherwise

9. On Detection of Multiple Object Instances Using Hough Transforms Probabilistic derivation Likelihood Term oAssume that given the existing objects y and the hypotheses assignments x, the distributions of the descriptors of voting elements are independent oLess crude than the independence assumption implicitly made by the traditional Hough Prior Term oOccam razor (or MDL) prior penalizes the number of the active hypotheses

10. On Detection of Multiple Object Instances Using Hough Transforms Probabilistic derivation 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 0 1 0 1 0 hypotheses how likely is that voting element belongs to an object Corresponds to the votes in standard Hough transform: Training stays the same! “MDL” prior: λ, if y h = 1 0, otherwise -∞ if x i = h, and y h = 0 0, otherwise voting elements Problem known as facility location [Delong et al. CVPR 2010] (today’s poster) looks at facility location with wider set of priors

11. On Detection of Multiple Object Instances Using Hough Transforms Probabilistic derivation 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 0 1 0 1 0 hypotheses voting elements oTried different methods for MAP- inference  belief propagation  simulated annealing oThey work well but don’t allow using large number of hypotheses  graph becomes huge and dense  sparsification heuristics required

12. On Detection of Multiple Object Instances Using Hough Transforms Probabilistic derivation 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 0 1 0 1 0 voting elements hypotheses oIf labeling of y is given the values of x i are independent oAfter maximizing out x we get: oLarge-clique, submodular oGreedy algorithm is as good as anything else (in terms of the approximation factor) oGreedy inference ~ iterative Hough voting

13. On Detection of Multiple Object Instances Using Hough Transforms Greedy maximization for our energy Greedily add detections starting from the empty set For each iteration 1.do the voting: oSet h 0 = the overall maximum of HoughImage 3.If HoughImage(h 0 ) > λ, add h 0 to detection set, else terminate Sum over all voting elements Maximum over Hough votes for the hypotheses g that have already been switched on, including ‘background’ “standard” Hough vote for element i

14. On Detection of Multiple Object Instances Using Hough Transforms Inference Using the Hough forest trained in [Gall&Lempitsky CVPR09] Datasets from [Andriluka et al. CVPR 2008] (with strongly occluded pedestrians added)

15. On Detection of Multiple Object Instances Using Hough Transforms Results for pedestrians detection White = correct detection Green = missing object Red = false positive Our framework Hough transform + non-maximum suppression

16. On Detection of Multiple Object Instances Using Hough Transforms Results for pedestrians detection Blue = Hough transform + non-maximum suppression Light-blue = our framework Precision Recall Precision Recall TUD-crossing TUD-campus

17. On Detection of Multiple Object Instances Using Hough Transforms Results for lines detection Our framework Hough + NMS York Urban DB, Elder&Estrada ECCV 2008 oour framework is able to discern very close yet distinct lines, and is in general much less plagued by spurious detections

18. On Detection of Multiple Object Instances Using Hough Transforms Conclusion oFramework for detecting multiple objects, greedy inference ~ iterated Hough transform oNo need to find local maxima and suppress non-maxima – just take the only global maximum oProbabilistic model allows for extensions (ECCV paper coming: lines + vanishing points + horizon + zenith) oTraining stays the same as for the recent Hough-based framework oCode available at the project page: http://graphics.cs.msu.ru/en/ science/research/machinelearning/hough Thank you for your attention!