Abstract

Recently, the image-patch ordering method has been introduced in image processing. The method sorts patches of an image into a sequence so that on which we may apply 1-d signal processing technique. However, the sorting method above does not count the metric between the sorted data: All points on the sequence are uniformly arranged. In this talk, we introduce a 1-d manifold embedding model for the data sorting. In the model, we consider the data set residing on a curve in a high dimensional space. Then we isometrically map the data set onto a straight line so that a metric is defined on the data. Since the metric more precisely describes the similarity of the sorted data, when we apply interpolation, filtering, and other operators on the data, we will obtain more accurate results. We have applied the new model in handwritten digits classification and image inpainting and obtained better results than other existent methods.