LoFTR: Detector-Free Local Feature Matching with Transformers

LoFTR: Detector-Free Local Feature Matching with Transformers

Abstract

We present a novel method for local image feature matching. Instead of performing image feature detection, description, and matching sequentially, we propose to first establish pixel-wise dense matches at a coarse level and later refine the good matches at a fine level.

In contrast to dense methods that use a cost volume to search correspondences, we use self and cross attention layers in Transformer to obtain feature descriptors that are conditioned on both images. The global receptive field provided by Transformer enables our method to produce dense matches in low-texture areas, where feature detectors usually struggle to produce repeatable interest points

It’s a sign of John Dramani Mahama’s maturity as a writer that he is willing to consider his country’s future so _____: his memoir is appealingly honest, given to clear-eyed assessments rather than exaggerated accounts of achievements.

The evolution of sex ratios has produced, in most plants and animals with separate sexes, approximately equal numbers of males and females. Why should this be so? Two main kinds of answers have been offered. One is couched in terms of advantage to population. It is argued that the sex ratio will evolve so as to maximize the number of meetings between individuals of the opposite sex. This is essentially a “group selection” argument. The other, and in my view correct, type of answer was first put forward by Fisher in 1930. This “genetic” argument starts from the assumption that genes can influence the relative numbers of male and female offspring produced by an individual carrying the genes. That sex ratio will be favored which maximizes the number of descendants an individual will have and hence the number of gene copies transmitted. Suppose that the population consisted mostly of females: then an individual who produced sons only would have more grandchildren. In contrast, if the population consisted mostly of males, it would pay (对…有利) to have daughters. If, however, the population consisted of equal numbers of males and females, sons and daughters would be equally valuable. Thus a one-to-one sex ratio is the only stable ratio; it is an “evolutionarily stable strategy.” Although Fisher wrote before the mathematical theory of games had been developed, his theory incorporates the essential feature of a game—that the best strategy to adopt depends on what others are doing.

Since Fisher’s time, it has been realized that genes can sometimes influence the chromosome or gamete in which they find themselves so that the gamete will be more likely to participate in fertilization. If such a gene occurs on a sex-determining (X or Y) chromosome, then highly aberrant sex ratios can occur. But more immediately relevant to game theory are the sex ratios in certain parasitic wasp species that have a large excess of females. In these species, fertilized eggs develop into females and unfertilized eggs into males. A female stores sperm and can determine the sex of each egg she lays by fertilizing it or leaving it unfertilized. By Fisher’s argument, it should still pay a female to produce equal numbers of sons and daughters. Hamilton, noting that the eggs develop within their host—the larva of another insect—and that the newly emerged adult wasps mate immediately and disperse, offered a remarkably cogent analysis. Since only one female usually lays eggs in a given larva, it would pay her to produce one male only, because this one male could fertilize all his sisters on emergence. Like Fisher, Hamilton looked for an evolutionarily stable strategy, but he went a step further in recognizing that he was looking for a strategy.