The Quadratic-Chi Histogram Distance Family

We present a new histogram distance family, the Quadratic-Chi (QC). QC members are Quadratic-Form distances with a cross-bin χ2 -like normalization. The cross-bin χ2 -like normalization reduces the effect of large bins having undo influence. Normalization was shown to be helpful in many cases, where the χ2 histogram distance outperformed the L2 norm. However, χ2 is sensitive to quantization effects, such as caused by light changes, shape deformations etc. The Quadratic-Form part of QC members takes care of cross-bin relationships (e.g. red and orange), alleviating the quantization problem. We present two new crossbin histogram distance properties: Similarity-Matrix-Quantization-Invariance and Sparseness-Invariance and show that QC distances have these properties. We also show that experimentally they boost performance. QC distances computation time complexity is linear in the number of non-zero entries in the bin-similarity matrix and histograms and it can easily be parallelized. ...

• Type: Conference
• Year: 2010
• Where: ECCV
• Keywords: Computer Vision, ECCV 2010, Histogram Distance, QC Distances, QC Members