Large Lump Detection by SVM Sharmin Nilufar Nilanjan Ray

Outline Introduction Proposed classification method –Scale space analysis of LLD images –Feature for classification Experiments and results Conclusion

Introduction Large lump detection is important as it is related to downtime in oil- sand mining process. We investigate the solution of that problem by employing scale- space analysis and subsequent support vector machine classification. A frame with large lumpsA frame with no large lump

Feature extraction Supervised classification using Support Vector machine Proposed Method Image DoG Convolution Support Vector Machine Classification Result Training set and Test set Feature

Scale Space The scale space of an image is defined as a function, that is produced from the convolution of a variable- scale Gaussian, with an input image, I(x, y): where ∗ is the convolution operation in x and y, and –The parameter in this family is referred to as the scale parameter, –image structures of spatial size smaller than about have largely been smoothed away in the scale-space level at scale

Scale Space

Difference of Gaussian Difference of Gaussians (DoG) involves the subtraction of one blurred version of an original grayscale image from another, less blurred version of the original DoG can be computed as the difference of two nearby scales separated by a constant multiplicative factor k: Subtracting one image from the other preserves spatial information that lies between the range of frequencies that are preserved in the two blurred images.

Why Difference of Gaussian? DoG scale-space: Efficient to compute “Blob” characteristic is extracted from image Good theory behind DoG (e.g., SIFT feature)

Constructing Scale Space The scale space represents the same information at different levels of scale, To reduce the redundancy the scale space can be sampled in the following way: –The domain of the variable is discretized in logarithmic steps arranged in O octaves. –Each octave is further subdivided in S sub-levels. –At each successive octave the data is spatially downsampled by half. –The octave index o and the sub-level index s are mapped to the corresponding scale by the formula O is the number of Octaves O min index of the first octave S is the number of sub-levels is the base smoothing

Constructing Scale Space…

Scale Space Analysis of LL images

Scale Space Analysis of non-LL images

Feature From DoG One possibility is to use the DoG image (as a vector) for classification. Problem: this feature is not shift invariant. Remedy: construction of shift invariant kernel.

Shift Invariant Kernel: Convolution Kernel Given two images I and J, their convolution is given by: For LLD define a kernel between I and J as: This is the convolution kernel. Can we prove this is indeed a kernel? Note that this kernel function depends on parameters. How do we choose the parameter values?

Choosing Kernel Parameters Polynomial Kernel function on DoG training images without convolution Convolution kernel matrix on training DoG images The hint is there in the Gram matrix (aka kernel matrix): The right kernel matrix produces better result. Do you see any cue?

Choosing Kernel Parameters… Here’s one criterion for choosing a better Gram matrix: Look for a Gram matrix that is more “block-structured” Let be a Gram matrix, then consider a criterion: We can expect that for smaller values of r, K is more block-structured. So we can choose the parameter in K for which we obtain smallest r.

A Mixture Kernel A mixture kernel: We can prove that if K l are kernels, then K is also a kernel. Ex. Prove it. For the LLD problem, let’s consider a mixture kernel: Question: we want find out from the training data? How? We can minimize r as a function of Another such criterion is called kernel alignment criterion. This is a very active area of research these days.

Supervised Classification Classification Method- Support Vector Machine (SVM) with polynomial kernel –Using cross validation we got polynomial kernel of degree 2 gives best results. Training set -20 image –10 large lump images –10 non large lump images Test Set images (training set including) –45 large lumps

Experimental Results Without convolution the system can detect 40 out of 45 large lump. FP - No large lump but system says lump FN - There is a large lump but system says no Precision=TP/(TP+FP)=40/(40+72)=0.35 Recall= TP/(TP+FN) =40/(40+5)=0.89

Experimental Results With convolution the system can detect 42 out of 45 large lump. FP - No large lump but system says lump FN - There is a large lump but system says no Precision=TP/(TP+FP)=42/(42+22)=0.66 Recall= TP/(TP+FN) =42/(42+3)=0.94

Conclusions Most of the cases DoG successfully captures blob like structure in the presence of large lump sequence LLD based on scale space analysis is very fast and simple No parameter tuning is required Shift invariant kernel improves the classification accuracy We believe by optimizing the kernel function we will achieve better classification accuracy (future work) The temporal information also can be used to avoid false positives (future work)

References [1]Huilin Xiong Swamy M.N.S. Ahmad, M.O., “Optimizing the kernel in the empirical feature space”, IEEE Transactions on Neural Networks, 16(2), pp , [2] G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, “Learning the kernel matrix with semidefinte programming,” J. Machine Learning Res., vol. 5, [3] N. Cristianini, J. Kandola, A. Elisseeff, and J. Shawe-Taylor, “On kernel target alignment,” in Proc. Neural Information Processing Systems (NIPS’01), pp. 367–373. [4] D. Lowe, "Object recognition from local scale-invariant features". Proceedings of the International Conference on Computer Vision pp. 1150–1157.,1999

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