Julie Peyronnet

Jean-Christophe C Roux

Julie Mamet

David Perrin

Joël Lachuer

Jean-Marc M Pequignot

Yvette Dalmaz

Dr Julie Peyronnet-Roux
email: j.peyronnet-roux@univ-cezanne.fr

Developmental plasticity of the carotid chemoafferent pathway in rats that are hypoxic

Keywords: prenatal stress, maturation, catecholamines, chemoreflex, breathing control Chemoafferent pathway plasticity and prenatal hypoxia

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Hypoxia during pregnancy represents a common problem during the foetal development, leading to numerous long-term adverse effects [START_REF] Okubo | Control of ventilation in adult rats hypoxic in the neonatal period[END_REF][START_REF] Nyakas | Hypoxia and brain development[END_REF][START_REF] Peyronnet | Prenatal hypoxia impairs the postnatal development of neural and functional chemoafferent pathway in rat[END_REF]2002;Carroll, 2003a;[START_REF] Perrin | Longterm prenatal hypoxia alters maturation of brain catecholaminergic systems and motor behavior in rats[END_REF].

In adult mammals, hypoxia increases ventilation through activation of the chemoafferent pathway. Hypoxemia is detected by peripheral chemoreceptors primarily located in the carotid bodies. This information is conveyed by chemoafferent fibres originating from the petrosal ganglion, and is integrated into discrete areas of the medulla oblongata containing catecholaminergic cell groups, i.e. mainly the nucleus tractus solitarius -caudal part -(A 2 C 2 c), the ventrolateral medulla (A 1 C 1 ), the ventrolateral pons (A 5 ) and the locus coeruleus in the pons (A 6 ) [START_REF] Finley | The central organization of carotid body afferent projections to the brainstem of the rat[END_REF][START_REF] Guyenet | Central respiratory control of A5 and A6 pontine noradrenergic neurons[END_REF][START_REF] Bianchi | Central control of breathing in mammals: neuronal circuitry, membrane properties, and neurotransmitters[END_REF]. Both medullary areas are respectively associated to the dorsal and the ventral respiratory groups [START_REF] Bianchi | Central control of breathing in mammals: neuronal circuitry, membrane properties, and neurotransmitters[END_REF]. These catecholaminergic brainstem areas participate in the control of breathing [START_REF] Guyenet | Central respiratory control of A5 and A6 pontine noradrenergic neurons[END_REF].

In rat neonates, the carotid body chemoreception pathway is immature.

Maturation of the carotid body occurs over the first few postnatal weeks (Eden & Hanson, 1987a;[START_REF] Hertzberg | Development of the arterial chemoreflex and turnover of the carotid body catecholamines in the newborn rats[END_REF][START_REF] Wang | Postnatal growth of the carotid body[END_REF] and any change in environmental O 2 modulates its development (Eden & Hanson, 1987b;[START_REF] Hertzberg | Ventilatory response to hyperoxia in newborn rats born in hypoxia -possible relationship to carotid body dopamine[END_REF][START_REF] Gauda | Maturation of peripheral arterial chemoreceptors in relation to neonatal apnoea[END_REF][START_REF] Bavis | Developmental plasticity of the hypoxic ventilatory response after perinatal hyperoxia or hypoxia[END_REF][START_REF] Donnelly | Development of carotid body/petrosal ganglion response to hypoxia[END_REF]. Concerning catecholaminergic medullary areas, maturation of the nucleus tractus solitarius and ventrolateral medulla [START_REF] Vincent | Postnatal development of rat nucleus tractus solitarius neurons: morphological and electrophysiological evidence[END_REF][START_REF] White | Ontogeny of the O 2 -sensitive pathway in medulla oblongata of postnatal rat[END_REF][START_REF] Roux | Neurochemical development of the brainstem catecholaminergic cell groups in rat[END_REF], of A 5 [START_REF] Di Pasquale | Serotonergic modulation of the respiratory rhythm generator at birth: an in vitro study in the rat[END_REF] and of A 6 [START_REF] Bezin | Postnatal development of the tyrosine hydroxylase-containing cell population within the rat locus coeruleus: topological organisation and phenotypic plasticity[END_REF] develops within the first two-three postnatal weeks.

Neonatal [START_REF] Slotkin | Effects of neonatal hypoxia on brain development in the rat: immediate and longterm biochemical alterations in discrete regions[END_REF] or prenatal [START_REF] Nyakas | Hypoxia and brain development[END_REF] hypoxic exposure impairs the postnatal development and synaptogenesis of brain areas and we previously reported that prenatal hypoxia impairs the brainstem control of breathing of juvenile and adult rats [START_REF] Peyronnet | Prenatal hypoxia impairs the postnatal development of neural and functional chemoafferent pathway in rat[END_REF].

The purpose of this study was to evaluate the effect of prenatal hypoxia on the maturation of the chemoafferent pathway from birth to adulthood with a particular attention to the first week of life. Ontogenesis of the chemoafferent neural circuits following prenatal hypoxia was investigated using cellular and physiological tools.

We assessed the effects of prenatal hypoxia (10% O 2 from day to day 20 of gestation) on male offspring at birth (P0) and on postnatal (P) days 3, 7, and 68. We determined the postnatal maturation of the respiratory control system by analysing the in vivo TH activity in the carotid body, the petrosal ganglion and the A C 2 c, A 1 C 1 , A 5 and A 6 brainstem cell groups. The physiological sequelae were evaluated on the development of the resting ventilation and the hypoxic ventilatory response.

MATERIALS AND METHODS

Hypoxia during pregnancy

Twenty-four pregnant rats (Sprague-Dawley, IFFA CREDO, l'Arbresle, France) were exposed to hypoxia (10% O 2 , 90% N 2 ) from day 5 to day 20 of gestation as previously described [START_REF] Peyronnet | Prenatal hypoxia impairs the postnatal development of neural and functional chemoafferent pathway in rat[END_REF]. On day 20 of gestation, pregnant rats were housed individually and birth occurred in normoxia. At birth, all hypoxic pups were mixed and redistributed randomly to nursing females which had never been exposed to hypoxic conditions to avoid any possible effects of hypoxia on the quality of the milk and to minimise litter-to-litter variations. To ensure a common nutritional status, each nursing group contained 10-11 pups. Dams, which had been exposed to hypoxia, were no longer needed for this experiment. Hypoxic pups were identified according to their postnatal age and not according to their litters. Experiments were performed using only male pups in order to avoid gender parameter. All animals grew up in normoxia. These offspring constituted the prenatal hypoxic group (PH). The control group of rats was composed of pups delivered by normoxic mothers, whose gestation occurred under normoxic conditions in a similar Plexiglas chamber (21% O 2 ), mixed and redistributed randomly at birth to the normoxic mothers. All experiments were carried out according to the ethical principles laid down by the French (Ministère de l'Agriculture) and EU Council Directives for care of laboratory animals (N°02889).

Plethysmography

Ventilation was measured in awake unrestrained prenatal hypoxic and control rats at birth (P0), and on postnatal day 3 (P3), 7 (P7), 21 (P21) and (P68), using barometric plethysmography. According to the protocol described previously [START_REF] Peyronnet | Prenatal hypoxia impairs the postnatal development of neural and functional chemoafferent pathway in rat[END_REF]. The volume of the Plexiglas chambers was 0.22 l for the P0, P3 and P7 pups, 0.75 l for the P21 offspring and 5.4 l for the P68 rats, and calibration of the chambers was done before placing the animal in the box in order to avoid signal interferences between calibration and ventilation of the animal. Alternately, a control or a prenatal hypoxic rat was placed in the chamber for measurements of ventilation. Tidal volume (V T ), respiratory frequency (f) and minute ventilation (V E ) were calculated from breathby-breath records over 30-50 consecutive cycles (around 30 s) by computer analysis of the spirogram. V T was calculated by measuring the amplitude of the signal and not the area under the curve. V E , V T and f were respectively expressed in ml.min -1 , ml and min - 1 . All measurements in normoxia were performed in quadruplet. The mean of these 4 values was considered as the basal ventilation. The hypoxic test was then carried out by flushing the plethysmograph chamber with a mixture of 10% O 2 and 90% N 2 . After the 10% O 2 level was reached (within 10 seconds for the bigger volume) inside the chamber, the system was sealed to perform the measurements (1 min and 4 min after the beginning of hypoxia) of the hypoxic ventilatory response (HVR) involving 40 to 60 breath cycles in order to avoid CO 2 accumulation. Between the tests performed at 1 min and 4 min, the system was re-opened and the cage flushed with the hypoxic mixture. In order to collect correct data concerning V T , we made sure all recordings were realised at an ambient temperature corresponding to thermoneutrality at each age group. The condition known as thermoneutrality is the range in ambient temperature over which body temperature is maintained with minimal metabolic effort. Furthermore, small variations of the ambient temperature lead to fluctuating values concerning V T . This is especially true for small rodents. If necessary, the gas (air or hypoxia) was heated or cooled down before its entry in the plethysmograph. The set point of ambient temperature (thermoneutrality) was strictly the same for prenatal hypoxic rats and for controls. Finally, V T calculation remains an estimation and we do not interpret its absolute value. V T calculation is just used as a means to compare prenatal normoxic and hypoxic rats.

Tissue dissection

Neurochemical assays and ventilation were performed on separate animals at P0, P3, P7, P21 and P68 in order to discard possible neurochemical changes resulting from the exposure to the brief hypoxic challenge used for respiratory measurements. Control and prenatal hypoxic offspring were sacrificed by cooling at birth, (8-10h after birth) and on postnatal day 3, and by cervical dislocation after deep anaesthesia with pentobarbital i.p. on postnatal days 7, 21, 68 (n = 10-12 in each group and at each age).

Excision of carotid bodies and petrosal ganglia was performed at each age under a dissection microscope. Petrosal ganglion and nodose ganglia were torn apart. Brains were rapidly removed from all animals. Each sample was frozen on dry ice and stored at microtome blade to the plane containing the point where the pyramidal decussation appears, serial coronal slices of the brains were cut. Thickness of the slices was adapted according to the rat ages determined proportionally to the brain size (128 µm at birth, 160 µm at P3, 192 µm at P7, 384 µm at P21, 480 µm at P68), so that the appearance of the different structures in relation with the number of sections could be constant.

Visualisation of the pyramidal decussation, the VII th cranial nerve pair, the inferior olive, the IV th ventricle, the cerebellum and the hippocampus was used as an anatomical point to confirm the relative position of the different areas. Moreover, we compared our different sections to [START_REF] Altman | Atlas of prenatal rat brain development[END_REF] developmental stereotaxic atlas. For the 21-and 68-day-old rats, cell groups were punched out according to the dissection procedure developed by [START_REF] Palkovits | Maps and guide to microdissection of the rat brain[END_REF] and adapted to young animals [START_REF] Roux | Neurochemical development of the brainstem catecholaminergic cell groups in rat[END_REF].

Neurochemistry

The in vivo TH activity can be used as a marker of the rate of catecholamine synthesis [START_REF] Carlsson | Simultaneous measurement of tyrosine and tryptophan hydroxylase activities in brain in vivo using an inhibitor of the aromatic amino acid decarboxylase. Naunym-Schmied[END_REF]. In vivo TH activity was estimated by measuring Ldihydroxyphenylalanine (L-DOPA) accumulation after inhibition of L-amino acid decarboxylase by NSD 1015 (3-hydroxybenzylhydrazine dichloride: Sigma, St Louis, USA). NSD 1015 was injected intraperitoneally (100 mg.kg -1 of body weight) 20 min before sacrifice. TH activity was expressed in picomoles of L-DOPA formed in 20 min and per pair of structures.

Total protein content can fluctuate unspecifically in physiological conditions, e.g., in response to circadian rhythms or chronic hypoxia [START_REF] Poncet | Chronic hypoxia affects peripheral and central vasoactive intestinal peptide-like immunoreactivity in the rat[END_REF]. Accordingly, the expression of the catecholamine activity per structure is more adequate than the expression of results per mg of protein in order to avoid artefactual variations of the catecholamine content and turnover following modifications of total protein levels in the structure.

Biochemical analyses

Structures were dissected out bilaterally and catecholamines were assayed on each pair of structures by high-performance liquid chromatography coupled with electrochemical detection. Tissues were disrupted by ultrasound in 100 μl 0.4 M (punches) or 0.1 M (carotid body, petrosal ganglion) perchloric acid containing 2.7 mM EDTA. In punch samples, the excess of perchloric acid was removed by addition of 8 μl 6.4 M potassium formiate to the supernatant. Homogenates were centrifuged (8,800g, 5 min) and a 20 μl aliquot of the supernatant was injected directly into a reverse phase column (ODS-Hypersil, 5 mm, 150 x 4.6 mm, Shandon, Cheshire, UK) containing a mobile phase (27 mM citric acid, 50 mM sodium acetate, 1 mM EDTA-Na 2 , 0.8 mM sodium acetyl sulfate and 8% methanol). The flow rate was 1.2 ml.min -1 . L-DOPA was measured at +0.72 V versus the Ag + /AgCl reference electrode (ELDEC 102, Chromatofield, Chateauneuf-les-Martigues, France). Detection limits, calculated by doubling the noise ratios and expressed in terms of picomoles of injected amounts, were less than 0.03 pmol for each compound and intra-assay coefficients were 0.2%.

Statistics

Neurochemical data are expressed as means ± S.E.M. For each structure, the effect of prenatal hypoxia was assessed using a two-way (prenatal hypoxia, age) analysis of variance (ANOVA) followed by Fisher's protected least square difference test.

Ventilatory data are expressed as means ± S.E.M. Because all studies were multivariate (prenatal hypoxia, age, time of hypoxic challenge), data were first subjected to global ANOVA. When a significant effect of treatment or interaction of treatment with age or hypoxic challenge was detected, lower order ANOVA was carried out to determine the time of hypoxic challenge or age of effect or interaction. In basal conditions, a twofactor ANOVA (prenatal hypoxia, age) was used to determine differences in ventilatory components between the prenatal and the control groups. The global response to hypoxia over 4 min was analysed using a three-factor ANOVA (prenatal hypoxia, age, hypoxic challenge). When interactions were significant, a post hoc test (Fisher's protected least square difference) was used to compare individual group. A P value <0.05 was considered to indicate statistical significance.

RESULTS

Prenatal hypoxia and body weight

As we previously reported [START_REF] Peyronnet | Long-lasting adverse effects of prenatal hypoxia on developing autonomic nervous system and cardiovascular parameters in rats[END_REF][START_REF] Perrin | Longterm prenatal hypoxia alters maturation of brain catecholaminergic systems and motor behavior in rats[END_REF], body weight of the prenatal hypoxic offspring was significantly reduced at P0, P3 and P7 but was similar to that of controls at P21 and P68 (Fig. 1).

Prenatal hypoxia and postnatal maturation of the afferent O 2 -sensing pathway (carotid body, petrosal ganglion).

Control rats: in the carotid body of control pups, the in vivo TH activity was high at birth (P0), it decreased during the first postnatal week compared to P0 (P3: -57%; P7: -61%) and increased thereafter to nearly reach the birth level at adulthood (Fig. 2).

In the petrosal ganglion of control pups, the development of TH activity was mainly characterised by a peak at P7 compared to P0 (P7: +163%) and a subsequent increase from the third week (Fig. 2).

Prenatal hypoxic rats: in the carotid body of prenatal hypoxic rats, the developmental pattern of the TH activity was altered compared to matched-age controls, with a decrease on postnatal day 3 (-25%) and 7 (-41%) and an increase on postnatal day 68 (+95%).

In the petrosal ganglion of prenatal hypoxic rats, the in vivo TH activity was decreased on postnatal day 7 (-40%) and increased on postnatal day 21 (+35%).

Prenatal hypoxia and postnatal maturation of catecholaminergic brainstem cell groups

The in vivo TH activity was measured in the A 1 C 1 , A 2 C 2 c, A 5 and A 6 cell groups in the brainstem from birth (P0) to postnatal day 68 (P68).

Control rats: in the A 1 C 1 , A 2 C 2 c, A 5 and A 6 cell groups of control rats, the postnatal development of the TH activity exhibited two marked increase in the TH activity (Fig. 2). The first increase was detected at P3 compared to P0 (A 2 C 2 c: +306%; A 1 C 1 : +227; A 5 : +190%) and at P21 compared to P7 (A 2 C 2 c: +584%; A 1 C 1 : +715; A 5 : +444%; A 6 : +77%). A second increase occurred at P21 compared to P7 (A 2 C 2 c: +584%; A 1 C 1 : +715%; A 5 : +444%; A 6 : +77%). In adult rats (P68), TH activity was lowered compared to the preceding age (P21) in A 2 C 2 c (-55%), A 1 C 1 (-65%) and A 5 (-70%) (Fig. 2). Thus, at P21, brainstem areas exhibited an intense peak in the TH activity, except in A 6 .

Prenatal hypoxic rats: prenatal hypoxia altered the developmental pattern of the in vivo TH activity (Fig. 2). Compared with the in vivo TH activity in matched-age control rats, this activity was increased in the brainstem areas during the first postnatal week (in A 2 C 2 c: +72% and +254% at P0 and P3 respectively, in A 1 C 1 : +174% and +32% at P3 and P7 respectively, in A 5 and A 6 +64% and + 29% at P3 respectively).

Later, TH activity was decreased in A 2 C 2 c (P21: -80%; P68: -15%), in A 1 C 1 (P21: -70%; P68:-16%) and in A 5 (P21:-70%) cell groups (Fig. 2).

The prenatal hypoxic exposure differently affects ontogenesis of the afferent O 2sensing pathway and of the catecholaminergic brainstem cell groups

Altogether, these data indicate that prenatal hypoxia induced, within the first week of life, a decrease in the TH activity in the carotid body and petrosal ganglia and an increase in the brainstem catecholaminergic cell groups (A 1 C 1 , A 2 C 2 c, A 5 and A 6 ) (Fig. 2). Later, we observed an increase in the TH activity in the carotid body and petrosal ganglion of prenatal hypoxic rats compared to control rats, whilst in the brainstem cell groups this activity was largely depressed compared to the control offspring. Two results have to be pointed out: i) for a given postnatal day, prenatal hypoxia elicited an inverse effect on the peripheral and central component, ii) for a given structure (carotid body, petrosal ganglion, A 2 C 2 c, A 1 C 1 or A 5 ), the prenatal hypoxic effect was reversed between the first and the third weeks (Fig. 2).

Prenatal hypoxia impairs postnatal breathing

Resting ventilation and hypoxic ventilatory response were measured in the control and prenatal hypoxic offspring at birth (P0) and on postnatal day 3, 7, 21 and 68 (Fig. 3).

Resting ventilation: compared to age-matched controls, prenatal hypoxia elicited basal increase in ventilation on postnatal day 0 (+33%), 3 (+38%), 7 (+35%) and 21 (+71%) (Fig. 3).The increase in the basal ventilation of the prenatal hypoxic animals was mainly due to a higher frequency for the 0-3-and 7-day-old pups (+24%, +26%, +13% respectively) and to a higher tidal volume for the 21-day-old rats (+96%).

Hypoxic ventilatory response; control rat: compared to respective basal values, hypoxic ventilatory response on the first minute of hypoxic exposure was characterised by a significant increase in the minute ventilation (P0: +63%; P3: +49%; P7: +43%; P21: +122%; P68: +51%) (Fig. 3), mainly due to an increase in the frequency. On the fourth minute of hypoxia the minute ventilation returned within the basal values for the 0-, 3-and 7-day-old offspring, reflecting the typical newborn biphasic response, and remained significantly increased for the 21-and 68-day-old rats (+137% and +83% respectively) (Fig. 3).

Hypoxic ventilatory response; prenatal hypoxic rats: compared to respective basal values, the minute ventilation was increased on the first minute of hypoxia, except for the 7-day-old offspring, (P0: +46%; P3: +46%; P21: +134%; P68: +68%) (Fig. 3), mainly due to an increased frequency. Four minutes of hypoxic challenge sustained the initial increase in the minute ventilation compared to basal values (P0:+46%; P3: +46%, P21: 132%; P68: +78%). Therefore, the biphasic newborn response observed in control rats within the first week of age was not evidenced in the prenatal hypoxic pups. At the end of the hypoxic exposure, the minute ventilation set at a higher level in the 3-, 7-and 21-day-old prenatal hypoxic rats compared to the matched-age control animals (+51%, +61% and +67% respectively), due to an increased frequency on P3 and an increased tidal volume on P7 and P21. Most of the altered ventilatory parameters were resolved at P68 (Fig. 3).

DISCUSSION

The present study shows that a two-week prenatal hypoxic exposure alters the maturation of the afferent O 2 -sensing pathway (carotid body and petrosal ganglion) and the brainstem catecholaminergic cell groups (A 2 C 2 c, A 1 C 1 , A 5 et A 6 cell groups) involved in the regulation of breathing. Because of the postnatal maturation of the chemoafferent pathway, this study focused on the first three weeks of life. To the best of our knowledge, this is the first study combining a longitudinal analysis of neurochemical and physiological events related to breathing in response to a common prenatal environment. Our data show that, after prenatal hypoxia, i) the developmental change of the in vivo TH activity is tissue-specific with an opposite effect on the afferent O 2 -sensing pathway and on the brainstem catecholaminergic cell groups, ii) a shift of the effect of prenatal hypoxia occurs between 1 and 3 weeks indicating that the period between the first and the third postnatal weeks is important for the development of the chemoafferent pathway, iii) ventilation is increased in normoxia and in hypoxia and there is no evidence for the biphasic response to hypoxia.

Experimental comments

In the present study, only males were retained to avoid female hormonal effect on ventilation [START_REF] Joseph | Gender differentiation of the chemoreflex during growth at high altitude: functional and neurochemical studies[END_REF][START_REF] Bavis | Developmental plasticity of the hypoxic ventilatory response in rats induced by neonatal hypoxia[END_REF]. The duration of exposure to hypoxia was quite long (E5-E20) compared to most of the studies in rats referring to short perinatal hypoxia/ischemia. This model of mild and long-term prenatal hypoxia mimics pathological hypoxic situations in pregnant women. Although the degree of foetal hypoxemia caused by exposure of the pregnant rats to hypoxia cannot be evaluated, we previously showed that these experimental conditions increased the maternal haematocrit (75 ± 6% vs. 51 ± 1%) and the expression of HIF-1α in the foetal brain, which indicates a characteristic adaptive response to hypoxemia [START_REF] Royer | Effects of gestational hypoxia on mRNA levels of Glut3 and Glut4 transporters, hypoxia inducible factor-1 and thyroid hormone receptors in developing rat brain[END_REF]. Furthermore, in sheep and goats, a prenatal hypoxic stress, with a similar level of oxygen tension, was able to decrease foetal PaO 2 and to stimulate the carotid chemoreflex pathway [START_REF] Nitsos | The distribution of FOS-immunoreactive neurons in the brainstem, midbrain and diencephalon of fetal sheep in response to acute hypoxia in mid and late gestation[END_REF].

Ventilation was evaluated using whole body plethysmography. The accuracy of V T calculation based on whole body plethysmography data has been questioned, especially in newborns [START_REF] Enhorning | Whole-body plethysmography, does it measure tidal volume of small animals[END_REF]. The absolute V T and V E values should be viewed with caution, but they were appropriately used to compare control and prenatal hypoxic data resulting from the same experimental design. Neurochemical assays and ventilation were performed on separate animals at P0, P3, P7, P21 and P68 in order to discard possible changes in the neural pathway activity resulting from the exposure to the brief hypoxic challenge used for respiratory measurements.

Ontogenesis of the in vivo TH activity of the chemoreflex pathway in normoxia

The data indicate that the pattern of postnatal development of the TH activity within structures in the chemoafferent pathway is not homogeneous and undergoes changes according to the tissues.

In carotid bodies of control animals, the present study reveals a decline in TH activity within the first postnatal week. Among the numerous neurotransmitters present in the neurosecretory type I cells of the carotid body, catecholamines and especially dopamine has received the most attention [START_REF] Gonzalez | Carotid body chemoreceptors: from natural stimuli to sensory discharges[END_REF][START_REF] Bairam | Neurotransmitters in carotid body development[END_REF]. The carotid body in the foetus is well adapted to the low O 2 tension in utero.

Postnatal maturation of the carotid body is dependent on environmental oxygen supply (Carroll, 2003b;[START_REF] Donnelly | Development of carotid body/petrosal ganglion response to hypoxia[END_REF][START_REF] Wang | Postnatal growth of the carotid body[END_REF]. At birth, when suddenly exposed to a relative high O 2 level, the carotid body changes its dopamine metabolism by decreasing the dopamine turnover and the mRNA encoding TH [START_REF] Hertzberg | Development of the arterial chemoreflex and turnover of the carotid body catecholamines in the newborn rats[END_REF][START_REF] Bairam | Neurotransmitters in carotid body development[END_REF]. This neurochemical resetting is partly involved in the postnatal resetting of carotid body O 2 sensitivity [START_REF] Holgert | Functional and developmental studies of the peripheral arterial chemoreceptors in rat: effects of nicotine and possible relation to sudden infant death syndrome[END_REF]. Our data on the developmental decrease in the TH activity extended previous results obtained on dopamine turnover and TH expression, and strengthened the evidence for a decline of the dopamine metabolism within the first postnatal week.

In the control petrosal ganglion containing the cell bodies of the afferent neurones, the in vivo TH activity increased within the first week. The data indicate that the developmental pattern in this ganglion is different from that observed in the carotid body. We propose that the catecholamine contents in the petrosal ganglion could be non-limiting in order to convey the carotid body inputs. Indeed, it has been earlier

shown that developmental changes in cell characteristics of the petrosal ganglion are small and are unlikely to account for the developmental increase in chemoreceptor responsiveness with age [START_REF] Donnelly | Developmental changes in membrane properties of chemoreceptor afferent neurons of the rat petrosal ganglia[END_REF].

In central areas, the development of TH activity is characterised by two different increases, the first occurring between P0-P3, the second between P7-P21. Enhanced TH activity at P3 could result from the environmental changes induced by the transition from foetal to extra-uterine life [START_REF] Lagercrantz | The first breaths of air stimulate noradrenaline turnover in the brain of the newborn rat[END_REF]. Increase at P21 extended previous data obtained in the whole brainstem [START_REF] Coyle | Tyrosine hydroxylase in rat brain: developmental characteristics[END_REF]) and appeared to be specific to these catecholaminergic brainstem areas [START_REF] Perrin | Longterm prenatal hypoxia alters maturation of brain catecholaminergic systems and motor behavior in rats[END_REF]. Maturation of the brainstem sites takes between two to four weeks to complete [START_REF] White | Ontogeny of the O 2 -sensitive pathway in medulla oblongata of postnatal rat[END_REF][START_REF] Vincent | Postnatal development of rat nucleus tractus solitarius neurons: morphological and electrophysiological evidence[END_REF]. The second-third week is crucial for the developing rat brain because of changes in the energetic metabolism associated with the weaning period [START_REF] Clark | Development of enzymes of energy metabolism in the neonatal mammalian brain[END_REF]. Within this period numerous neuromodulators in the brainstem exhibit changes in their level of expression [START_REF] Wong-Riley | Neurochemical development of brainstem nuclei involved in the control respiration[END_REF]. This transient enhancement of the TH activity in most of the catecholaminergic brainstem nuclei at P21 could result from the activation of quiescent cells expressing the TH phenotype [START_REF] Bezin | Postnatal development of the tyrosine hydroxylase-containing cell population within the rat locus coeruleus: topological organisation and phenotypic plasticity[END_REF] in relation with the energetic needs. It might also be related to the maturation of the cardio-respiratory control [START_REF] Roux | Neurochemical development of the brainstem catecholaminergic cell groups in rat[END_REF][START_REF] Wong-Riley | Neurochemical development of brainstem nuclei involved in the control respiration[END_REF].

Prenatal hypoxia alters the ontogenesis of the TH activity of the chemoafferent pathway

In the carotid body, prenatal hypoxia amplified the developmental pattern of the TH activity changes reported in controls. Prenatal hypoxia enhanced the downregulation within the first postnatal week and increased the up-regulation in adulthood.

It has previously been shown that a postnatal hypoxic environment blunted the dopamine metabolism decline [START_REF] Hertzberg | Ventilatory response to hyperoxia in newborn rats born in hypoxia -possible relationship to carotid body dopamine[END_REF]. Since prenatal hypoxia enhanced the difference between the foetal and the postnatal oxygen tension [START_REF] Royer | Effects of gestational hypoxia on mRNA levels of Glut3 and Glut4 transporters, hypoxia inducible factor-1 and thyroid hormone receptors in developing rat brain[END_REF], we can postulate that this higher relative hyperoxia could be responsible for the higher adjustment and decline of the catecholamine metabolism. In the petrosal ganglion, as in the carotid body, prenatal hypoxia down-regulated the TH activity at P7 and upregulated it later (P21), thus indicating that prenatal hypoxia has the same effect on the TH activity in the cell bodies and in the peripheral sensitive nerve terminals.

Prenatal hypoxic exposure affects ontogenesis of the afferent O 2 -sensing pathway and of the brainstem catecholaminergic cell groups differently. In the brainstem cell groups, it amplified the increase in the TH activity observed in the control group at P3 and blunted the surge evidenced in the controls at P21, except in A 6 . Thus, the brainstem cell groups exhibited a TH activity which was up-regulated within the first postnatal week and down-regulated thereafter. At P3 and P21, the opposite effect of prenatal hypoxia on the peripheral and central components is conceivable since dopamine in the carotid body and noradrenaline in the brainstem are both inhibitory neuromodulators of breathing [START_REF] Gonzalez | Carotid body chemoreceptors: from natural stimuli to sensory discharges[END_REF]. It strongly suggests brainstem adjustment and compensation in response to the variation of the peripheral inputs.

Consistent with this proposal, the lack of peripheral inputs from the carotid bodies following carotid sinus nerve transection affects TH activity in medullary areas with a down-regulation and a subsequent up-regulation [START_REF] Roux | Ventilatory and central neurochemical reorganisation of O 2 chemoreflex after carotid sinus nerve transection in rat[END_REF]. Carotid bodies [START_REF] Donnelly | Prolonged apnea and impaired survival in piglets after sinus and aortic nerve section[END_REF] and BDNF/GDNF afferent inputs of the afferent fibres [START_REF] Katz | Regulation of respiratory neuron development by neurotrophic and transcriptional signaling mechanisms[END_REF] are essential for regulating the development of brainstem respiratory network. Altogether, these data suggest that variation of the peripheral inputs induces a central compensatory action/reaction and is involved in the remodelling of central catecholaminergic areas during development.

Prenatal hypoxia reveals an important period for maturation of the chemoafferent pathway

A two-week prenatal hypoxia revealed an important period for the postnatal development of the chemoafferent pathway. A shift of the effect of prenatal hypoxia occurred between 1 and 3 weeks. Before and after this stage, the modifications of the TH activity were reversed in both peripheral and central structures (down-regulation and subsequent up-regulation in carotid body and petrosal ganglion, up-regulation and subsequent down-regulation in A 2 C 2 c, A 1 C 1 or A 5 ). Prenatal hypoxia strengthened the notion of an important period that we showed with TH measurement in central areas of controls and extended it to the chemoafferent pathway.

Chronic hyperoxia [START_REF] Bavis | Critical developmental period for hyperoxia-induced blunting of hypoxic phrenic responses in rats[END_REF] or acute hypoxic challenge [START_REF] Liu | Postanal changes in ventilation during normoxia and acute hypoxia in the rat: implication for a sensitive period[END_REF]) also revealed a sensitive period in the breathing and neural control mechanisms occurring around the second postnatal week. This important period for the development of the chemoafferent pathway, evidenced in this study after prenatal hypoxia, can be related to several morphological and electrophysiological phases of synaptic maturation occurring in the nucleus tractus solitarius and ventrolateral medulla [START_REF] White | Ontogeny of the O 2 -sensitive pathway in medulla oblongata of postnatal rat[END_REF][START_REF] Liu | Postnatal changes in cytochrome oxidase expressions in brain stem nuclei of rats: implications for sensitive periods[END_REF]. A developmental imbalance between neurochemical excitatory and inhibitory systems in the brainstem occurs at the end of the second postnatal week [START_REF] Wong-Riley | Neurochemical development of brainstem nuclei involved in the control respiration[END_REF]. Our study also evidenced a temporal imbalance of the involvement of the catecholaminergic structures related to the chemoafferent pathway.

Prenatal hypoxia alters postnatal breathing

Data of the prenatal hypoxic group of animals showed increased ventilation in normoxia as in response to a hypoxic test but no biphasic response to hypoxia.

Ventilation undergoes significant maturational changes in the postnatal period [START_REF] Liu | Postanal changes in ventilation during normoxia and acute hypoxia in the rat: implication for a sensitive period[END_REF] and perinatal environment plays a critical role in shaping ventilation and respiratory control [START_REF] Bavis | Critical developmental period for hyperoxia-induced blunting of hypoxic phrenic responses in rats[END_REF][START_REF] Bavis | Developmental plasticity of the hypoxic ventilatory response in rats induced by neonatal hypoxia[END_REF][START_REF] Bavis | Developmental plasticity of the hypoxic ventilatory response after perinatal hyperoxia or hypoxia[END_REF]Carroll, 2003a;[START_REF] Mortola | Implications of hypoxic hypometabolism during mammalian ontogenesis[END_REF][START_REF] Donnelly | Development of carotid body/petrosal ganglion response to hypoxia[END_REF]. The increased basal ventilation in normoxia and the lack of the biphasic response to hypoxia of offspring prenatally exposed to hypoxia might represent a shift in the balance of the excitatory action of carotid body chemoreceptors [START_REF] Lahiri | Arterial PO2 and PCO2 stimulus threshold for carotid chemoreceptors and breathing[END_REF] and inhibitory effect of central pathways (Eden & Hanson, 1987ab;[START_REF] Fung | Characterization of ventilatory responses to hypoxia in neonatal rats[END_REF][START_REF] Bissonnette | Mechanisms regulating hypoxic respiratory depression during fetal and postnatal life[END_REF]. Whilst the role of dopamine in the carotid body function is still questioned in vivo [START_REF] Gonzalez | Carotid body chemoreceptors: from natural stimuli to sensory discharges[END_REF][START_REF] Donnelly | Development of carotid body/petrosal ganglion response to hypoxia[END_REF], the carotid body exerts a vital influence when the medullary control is immature and then switch from a vital to a regulatory role after complete maturation of the central autonomic areas.

For small animals, important factors influencing the response to hypoxia are body weight and metabolic rate [START_REF] Mortola | Metabolic and ventilatory interaction in the newborn[END_REF][START_REF] Mortola | Implications of hypoxic hypometabolism during mammalian ontogenesis[END_REF]. We previously reported that these prenatal 7-day-old hypoxic pups did not exhibit the reduced oxygen consumption observed in controls in response to a postnatal hypoxic exposure [START_REF] Peyronnet | Prenatal hypoxia impairs the postnatal development of neural and functional chemoafferent pathway in rat[END_REF]. We cannot exclude that the lack of the decline in ventilation over the course of the hypoxic challenge observed in the prenatal hypoxic offspring until P7 might not partly result from their lack of hypoxic hypometabolism [START_REF] Peyronnet | Prenatal hypoxia impairs the postnatal development of neural and functional chemoafferent pathway in rat[END_REF].

Among the numerous neuromodulators involved in breathing and the hypoxic ventilatory response [START_REF] Bianchi | Central control of breathing in mammals: neuronal circuitry, membrane properties, and neurotransmitters[END_REF], the role of monoamines in the respiratory control is established [START_REF] Guyenet | Central respiratory control of A5 and A6 pontine noradrenergic neurons[END_REF]. The altered developmental evolution of the TH activity after prenatal hypoxia can be considered as a neuronal marker of the central reorganisation involved in this new ventilatory pattern. In conclusion, by using a double approach, both cellular (TH activity) and functional (ventilation), this study is the first to demonstrate that prenatal hypoxia alters the activity of the chemoafferent pathway, from birth, with lasting postnatal cellular and functional sequelae.

Implications for humans

In humans, several pathophysiological situations are associated with a deficit in oxygen supply for the foetus, such as maternal anaemia, hypertension, reduced placenta size, pre-eclampsia, smoking, reduced oxygen supply in high altitude. Our data may be relevant to understand clinical syndromes during the neonatal period. In the Sudden Infant Death Syndrome (SIDS), impaired pattern in respiratory activity [START_REF] Gordon | Sudden infant death syndrome: abnormalities in short term fluctuations in heart rate and respiratory activity[END_REF][START_REF] Schechtman | Correlations between cardiorespiratory measures in normal infants and victims of sudden infant death syndrome[END_REF], disappearance of catecholaminergic markers in A 1 C 1 /A 2 C 2 c [START_REF] Obonai | Catecholamine neurons alteration in the brainstem of sudden infant death syndrome victims[END_REF] and activation of the dopamine metabolism in carotid bodies [START_REF] Perrin | Sudden infant death syndrome: increased carotid-body dopamine and noradrenaline content[END_REF] have been reported. Carotid chemoreflex plays a critical role in the survival of newborns by protecting them against prolonged apnoeas [START_REF] Donnelly | Prolonged apnea and impaired survival in piglets after sinus and aortic nerve section[END_REF]) and failure of the development of functional chemoreceptors [START_REF] Gauda | Maturation of peripheral arterial chemoreceptors in relation to neonatal apnoea[END_REF][START_REF] Cohen | Development of chemoreceptors in infants[END_REF] has been evoked in breathing dysfunction in infants. The present prenatal hypoxic protocol in rats appears particularly relevant in order to better understand the neurochemical pathogenesis of these developmental disorders.

FIG. 1 .

 1 FIG.1. Long term effects of the prenatal hypoxic treatment on the body weight. Data are expressed as means ± S.E.M. at birth (P0) postnatal day 3, 7, 21 and 68. Significant differences between normoxic (Control) and prenatal hypoxic (PH) groups of rats (**P <0.01, ***P <0.001).

Acknowledgements

This work was supported by the CNRS, the University Claude Bernard Lyon 1, and the Région Rhone-Alpes (France). The skilful technical assistance of J. Péquignot was greatly appreciated.

Abbreviations

ANOVA, analysis of variance; CB, carotid body; f, frequency; min, minute; HVR, hypoxic ventilatory response; PG, petrosal ganglion; S.E.M., standard error of the mean; TH, tyrosine hydroxylase; V E , minute ventilation; V T , tidal volume.


Sara Akodad
email: sara.akodad@ims-bordeaux.fr

Lionel Bombrun
email: lionel.bombrun@ims-bordeaux.fr

Charles Yaacoub
email: charlesyaacoub@usek.edu.lb

Yannick Berthoumieu
email: yannick.berthoumieu@ims-bordeaux.fr

Christian Germain
email: christian.germain@ims-bordeaux.fr

Image classification based on log-Euclidean Fisher Vectors for covariance matrix descriptors

Keywords: Fisher vector, vector of locally aggregated descriptors, log-Euclidean metric, covariance matrices, SIFT descriptors, deep neural network, classification

This paper introduces an image classification method based on the encoding of a set of covariance matrices. This encoding relies on Fisher vectors adapted to the log-Euclidean metric: the log-Euclidean Fisher vectors (LE FV). This approach is next extended to full local Gaussian descriptors composed by a set of local mean vectors and local covariance matrices. For that, the local Gaussian model is transformed to a zero-mean Gaussian model with an augmented covariance matrix. All these approaches are used to encode handcrafted or deep learning features. Finally, they are applied in a remote sensing application on the UC Merced dataset which consists in classifying land cover images. A sensitivity analysis is carried out to evaluate the potential of the proposed LE FV.

I. INTRODUCTION

The goal of a supervised classification algorithm is to label an image with one class name depending on its content. The leading approaches in the beginning of the 2000s were based on feature coding. These approaches include the bag of words model (BoW) [START_REF] Sivic | Discovering objects and their location in images[END_REF], the vector of locally aggregated descriptors (VLAD) [START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF], [START_REF] Arandjelović | All about VLAD[END_REF] and the Fisher vectors (FV) [START_REF] Perronnin | Fisher kernels on visual vocabularies for image categorization[END_REF], [START_REF] Perronnin | Improving the Fisher kernel for large-scale image classification[END_REF], [6]. All these approaches have been successfully validated in a wide variety of applications such as image classification [START_REF] Perronnin | Fisher kernels on visual vocabularies for image categorization[END_REF], [START_REF] Douze | Combining attributes and Fisher vectors for efficient image retrieval[END_REF], [START_REF] Sánchez | Image classification with the Fisher vector: Theory and practice[END_REF], text retrieval [START_REF] Salton | Term-weighting approaches in automatic text retrieval[END_REF], action and face recognition [START_REF] Faraki | More about VLAD: A leap from Euclidean to Riemannian manifolds[END_REF], etc.

Since 2012, Convolutional Neural Networks (CNN) have become a standard for image classification problems [START_REF] Le Cun | Handwritten digit recognition with a backpropagation network[END_REF], [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF]. Since then, in order to take advantage of both approaches (deep neural network architecture and FV descriptors), many authors have proposed hybrid classification algorithms which combine them. For example, a network of fully connected layers has been trained on the FV descriptors in [START_REF] Perronnin | Fisher vectors meet neural networks: A hybrid classification architecture[END_REF]. The deep Fisher network composed by stacking several FV layers is another hybrid architecture [START_REF] Simonyan | Deep fisher networks for large-scale image classification[END_REF]. Inspired by the VLAD image representation, the NetVLAD has been proposed in [START_REF] Arandjelovic | Netvlad: CNN architecture for weakly supervised place recognition[END_REF] to mimick a VLAD layer. Other approaches include the FV or VLAD encoding of CNN features from different layers of the network [START_REF] Ng | Exploiting local features from deep networks for image retrieval[END_REF], [START_REF] Cimpoi | Deep filter banks for texture recognition, description, and segmentation[END_REF], [START_REF] Diba | Deep visual words: Improved fisher vector for image classification[END_REF], [START_REF] Li | Integrating multilayer features of convolutional neural networks for remote sensing scene classification[END_REF].

Recently, many works are dedicated to extend the formalism of encoding to features lying in a non-Euclidean space. This is for example the case of covariance matrices that have already proved their interest in many classification problems [START_REF] Faraki | More about VLAD: A leap from Euclidean to Riemannian manifolds[END_REF], [START_REF] Formont | Statistical classification for heterogeneous polarimetric SAR images[END_REF], [START_REF] Barachant | Classification of covariance matrices using a Riemannian-based kernel for BCI applications[END_REF], [START_REF] Said | Texture classification using Rao's distance on the space of covariance matrices[END_REF]. But, since covariance matrices are symmetric positive definite (SPD) matrices, standard Euclidean calculus are not adapted. The use of the geometrical information can lead to more accurate representation of the inherent structure of these observed covariance matrices. Since then, the Riemannian geometry has become increasingly popular in the computer vision community. When dealing with covariance matrices, two Riemannian metrics are generally considered: the log-Euclidean and the affine-invariant Riemannian metric. Recently, some authors have proposed to use these metrics in order to extend the BoW and VLAD descriptors. This yields to the so-called log-Euclidean bag of words (LE BoW) [START_REF] Yuan | Human action recognition under log-Euclidean Riemannian metric[END_REF], [START_REF] Faraki | Log-euclidean bag of words for human action recognition[END_REF], bag of Riemannian words (BoRW) [START_REF] Faraki | Fisher tensors for classifying human epithelial cells[END_REF], log-Euclidean vector of locally aggregated descriptors (LE VLAD) [START_REF] Faraki | More about VLAD: A leap from Euclidean to Riemannian manifolds[END_REF] and intrinsic Riemannian vector of locally aggregated descriptors (RVLAD) [START_REF] Faraki | More about VLAD: A leap from Euclidean to Riemannian manifolds[END_REF]. Recently, we have proposed to extend the FV descriptors to SPD features. This has involved the Log-Euclidean Fisher vectors (LE FV) and the Riemannian Fisher vectors (RFV) [START_REF] Ilea | Texture image classification with Riemannian Fisher vectors[END_REF], [START_REF] Ilea | Covariance matrices encoding based on the log-Euclidean and affine invariant Riemannian metrics[END_REF], [START_REF] Ilea | Fisher vector coding for covariance matrix descriptors based on the log-Euclidean and affine invariant Riemannian metrics[END_REF]. Although the log-Euclidean metric do not yield full affine invariance compared to the affine invariant Riemannian metric, it is invariant by similarity (orthogonal transformation and scaling). These characteristics allow to reduce the computation time while maintaining comparable performance with methods based on the affine invariant Riemannian metric. Nevertheless, all these coding methods are only valid for covariance matrix descriptors. Here, we propose to extend these methods to full local Gaussian descriptors that are composed of local means and local covariance matrices.

The main contributions of the paper are threefold. First, we present how FV can be used to encode a set of covariance matrix by using the log-Euclidean metric. Next, we extend this encoding to full local Gaussian descriptors. The proposed approach relies on an augmented SPD matrix which represents both the local means and the covariance matrices [START_REF] Lovric | Multivariate normal distributions parametrized as a riemannian symmetric space[END_REF], [START_REF] Huang | Log-Euclidean metric learning on symmetric positive definite manifold with application to image set classification[END_REF], [START_REF] Harandi | Dimensionality reduction on SPD manifolds: The emergence of geometry-aware methods[END_REF]. And finally, we propose an hybrid deep-learning architecture which allows to encode CNN features with the proposed LE FV.

The paper is structured as follows. Section II recalls the general principle of a classification algorithm based on FV. Section III introduces the proposed LE FV descriptor and its adaptation to full local Gaussian descriptors. An application of these descriptors to the classification of remote sensing images is presented in Section IV. Section V introduces an hybrid deep learning architecture based on the encoding of CNN layers with the LE FV. And finally, Section VI synthesizes the main conclusions of this work.

II. VLAD AND FISHER VECTORS ENCODING OF SIFT

DESCRIPTORS

In this section, we present the very conventional approach which consists in encoding handcrafted features such as scale invariant feature transform (SIFT) descriptors [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF] with the Fisher vectors (FV) [START_REF] Perronnin | Fisher kernels on visual vocabularies for image categorization[END_REF], [START_REF] Perronnin | Improving the Fisher kernel for large-scale image classification[END_REF], [6] or with the vector of locally aggregated descriptors (VLAD) [START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF]. This approach has been successfully used in a wide variety of image processing applications [START_REF] Perronnin | Fisher kernels on visual vocabularies for image categorization[END_REF], [START_REF] Douze | Combining attributes and Fisher vectors for efficient image retrieval[END_REF], [START_REF] Sánchez | Image classification with the Fisher vector: Theory and practice[END_REF], [START_REF] Salton | Term-weighting approaches in automatic text retrieval[END_REF], [START_REF] Faraki | More about VLAD: A leap from Euclidean to Riemannian manifolds[END_REF]. The global principle of this approach is presented in Fig. 1. It consists in the following steps:

1) Data splitting: At the beginning, data are separated into two disjoints sets used respectively for training and testing.

2) Feature extraction: An handcrafted features extraction step is then applied, with for example SIFT descriptors. This latter allows to obtain feature vectors invariant to scale, rotation, translation, and partially invariant to illumination. The SIFT algorithm is achieved through two stages. First, a detection algorithm is applied to detect keypoints in the image. Then, the SIFT descriptor x is computed for each detected keypoint. In the end, each image is represented by a set of N SIFT descriptors x i of dimension 128.

p(x t |λ) = K i=1 ω k p k (x t |λ), (1)
where, for each cluster k:

p k (x t |λ) = exp{-1 2 (x t -µ k ) T Σ -1 k (x t -µ k )} (2π) d/2 |Σ k | 1/2 , (2)
where The FV descriptor associated to X is obtained as the gradient of the sample log-likelihood with respect to the parameters of the GMM model, scaled by the inverse square root of the Fisher information matrix (FIM) F λ :

(•) T is the transpose operator, | • | is the deter- minant, ω k ∈ (0, 1), µ k ∈ R d , Σ k ∈ P d the
G X λ = F -1 2 λ ∇ λ log p(X |λ). (3)
Next, by deriving with respect to the mean, the dispersion or the weight parameters, the following three FV are obtained:

G X µ d k = 1 √ ω k N n =1 γ k (x n ) x d n -µ d k σ d k , (4)
G X σ d k = 1 √ 2ω k N n =1 γ k (x n ) x d n -µ d k 2 σ d k 2 -1 , (5)
G X ω k = 1 √ ω k N n =1 γ k (x n ) -ω k , (6)
where µ d k (resp. σ d k ) is the d th element of vector µ k (resp. σ k ) and γ k (x n ) is the occupancy probability of x n to the k-th Gaussian component, also named the posterior probability, and is defined as:

γ k (x n ) = ω k p k (x n |λ k ) K j=1 ω j p j (x n |λ j ) . (7)
In the following, only the two gradients with respect to the mean µ d k and standard deviation σ d k are considered since the state-of-the-art in computer vision have shown that the best results are obtained with these FV [START_REF] Perronnin | Fisher kernels on visual vocabularies for image categorization[END_REF], [START_REF] Perronnin | Improving the Fisher kernel for large-scale image classification[END_REF], [6]. The VLAD descriptor has been introduced in [START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF] in a similar spirit to the FV. It can be interpreted as an hard version of the FV where only the derivative with respect to the mean is considered in [START_REF] Arandjelović | All about VLAD[END_REF]. The homoscedasticity assumption should also be made i.e. σ k = σ. To summarize, the VLAD encoding of X is obtained as the concatenation of vectors v k :

VLAD = [v T 1 , . . . , v T K ], (8)
where, for each atom of the codebook, the vector v k contains the sum of differences between the codeword and the feature samples assigned to it:

v k = xn∈c k x n -µ k . (9)
Once the FV or VLAD descriptors are computed, a postprocessing step is classically employed to improve the classification performance [START_REF] Perronnin | Improving the Fisher kernel for large-scale image classification[END_REF], [START_REF] Sánchez | Image classification with the Fisher vector: Theory and practice[END_REF]. It consists on a power and an 2 normalization. 5) Dimension reduction: Since the dimensionality of the feature space (FV or VLAD descriptors) can be high, a dimension reduction step can be considered to avoid the curse of dimensionality phenomenon. For that, different unsupervised or supervised dimension reduction techniques can be employed such as principal component analysis (PCA), linear discriminant analysis (LDA), Kernel discriminant analysis (KDA) to cite a few of them. 6) Classification: This final step consists on making a decision for each test image based on information contained in their vector representation (FV or VLAD). In practice, various classifiers can be employed such as k-nearest neighbors, support vector machine (SVM) or random forest.

III. LOG-EUCLIDEAN FISHER VECTORS FOR COVARIANCE MATRICES ENCODING

The objective of this section is to explain how the classification algorithm detailed in Section II can be adapted to local covariance matrix descriptors. Indeed, since covariance matrices are positive definite matrices, conventional tools developed in the Euclidean space are not well adapted to these observations. The characteristics of the Riemannian geometry of the space P d of d×d symmetric and positive definite (SPD) matrices should be considered in order to obtain appropriate algorithms. Here, we address this point by considering the log-Euclidean metric.

A. Log-Euclidean Fisher Vectors (LE FV)

First, the covariance matrices of handcrafted features (such as SIFT descriptors calculated on a regular grid) are computed on a sliding window. It yields that each image is represented by a set M = {M n } n=1:N of covariance matrices M n ∈ P d . Employing the log-Euclidean metric to analyze these covariance matrices is equivalent to use the Euclidean metric on the log-Euclidean space. For that, each covariance matrix M n is first mapped on the log-Euclidean space by applying the matrix logarithm M LE n = log M n [START_REF] Faraki | Log-euclidean bag of words for human action recognition[END_REF], [START_REF] Arsigny | Log-Euclidean metrics for fast and simple calculus on diffusion tensors[END_REF], [START_REF] Rosu | Structure tensor Riemannian statistical models for CBIR and classification of remote sensing images[END_REF]. Next, a vectorization operator is applied to obtain the log-Euclidean vector representation. To summarize, the log-Euclidean vector representation of an SPD matrix M is the vector m ∈ R d(d+1) 2

defined as m = Vec(log(M)) where Vec is the vectorization operator defined as:

Vec(X) = X 11 , √ 2X 12 , . . . , √ 2X 1m , X 22 , √ 2X 23 , . . . , X mm , (10)
with X ij the elements of X. Now that SPD matrices are mapped on the log-Euclidean metric space, all the algorithms developed on the Euclidean space can be employed, in particular the FV and VLAD encoding which yield respectively to the so-called log-Euclidean FV (LE FV) [START_REF] Ilea | Covariance matrices encoding based on the log-Euclidean and affine invariant Riemannian metrics[END_REF] and log-Euclidean VLAD (LE VLAD) [START_REF] Faraki | More about VLAD: A leap from Euclidean to Riemannian manifolds[END_REF] descriptors.

Note that since dense SIFT descriptors may contain redundant information, the covariance matrices of these descriptors will not be well conditioned. To circumvent this and in order to reduce the dimension of the log-Euclidean vector representation m, a dimension reduction step such as PCA is applied on the handcrafted features as a pre-processing step. This step allows also to better fit the diagonal covariance matrix assumption made in Section II when deriving the FV, i.e. σ 2 k = diag(Σ k ). In the following, N P CA will refer to the number of retained principal components.

B. LE FV for full local Gaussian descriptors

In the previous subsection, only the local covariance matrix descriptor has been considered. In a full local Gaussian descriptor, the local mean vector can be jointly exploited with the local covariance matrix in order to increase the image representation within the classification task. Based on the works of [START_REF] Lovric | Multivariate normal distributions parametrized as a riemannian symmetric space[END_REF], the local Gaussian model can be transformed to a zero-mean Gaussian model with an augmented SPD matrix of dimension (d + 1) × (d + 1) given by:

M augmented = |M| -1 d+1 M + µµ T µ µ T 1 . ( 11
)
This approach has been successfully validated by many authors for image classification tasks [START_REF] Huang | Log-Euclidean metric learning on symmetric positive definite manifold with application to image set classification[END_REF], [START_REF] Harandi | Dimensionality reduction on SPD manifolds: The emergence of geometry-aware methods[END_REF]. Now that local mean and covariance matrix are embedded in a larger SPD matrix, the LE FV and LE VLAD descriptors can be computed for full local Gaussian descriptors by following the same strategy as the one described in Section III.

IV. APPLICATION TO REMOTE SENSING IMAGE

CLASSIFICATION

This section introduces an application to remote sensing image classification. For that, the UC Merced land use land In the following, a linear SVM classifier is considered for the final step in Fig. 1. The performance is evaluated in term of overall accuracy where half of the database is used for training while the remaining half is used for testing. In addition, three versions of FV descriptors are considered, i.e. by considering separately the derivative with respect to the mean µ d k , the dispersion σ d k or by fusing them, noted respectively F V (µ), F V (σ) and F V (µ+σ). One can observe that best performances are obtained for the VLAD and FV (when both derivatives are considered) descriptors with a similar behavior. In the following, only FV descriptor will be used.

A. Comparison between FV and VLAD encoding

B. Comparison between FV and LE FV

The purpose of this second experiment is to illustrate the potential of the proposed LE FV descriptor. For that, Fig. 3 draws the evolution of the classification accuracy for the FV (in blue) and the LE FV (in red). As observed, the best results are observed for the proposed LE FV illustrating the interest of local covariance matrix descriptor. A significant gain of about 6% if observed for the LE FV compared to FV. Note also that it does not require a large codebook, performances are quite stable with the codebook dimension.

In Fig. 4, we evaluate the influence of the number of retained principal components N P CA in the pre-processing step for K = 30. As observed, the dimension reduction greatly impacts the classification accuracy. It is hence necessary to find an optimal trade-off between performance and resources Descriptor Overall accuracy ± standard deviation FV [START_REF] Perronnin | Fisher kernels on visual vocabularies for image categorization[END_REF] 75.5 ± 1.3% LE FV 79.4 ± 1.3% LE FV augmented 80.1 ± 1.2% consumption in terms of computational time and memory space.

As explained in Section III-B, the local mean vector can be exploited jointly with the local covariance matrix to form an augmented SPD matrix. In order to evaluate the interest of this approach, Table 1 summarizes the classification performance obtained on the UC Merced dataset for the FV, LE FV and LE FV computed on the augmented SPD matrices for K = 30 and N P CA = 20. As observed the best classification result is obtained with these augmented descriptors illustrating the interest of a full local Gaussian descriptor.

V. LOG-EUCLIDEAN FISHER VECTORS IN AN HYBRID DEEP LEARNING ARCHITECTURE

A. FV encoding of CNN features

Now that the interest of the proposed LE FV has been observed for the classification of handcrafted features such Inspired by this approach, we propose to encode the output of the convolutional layers with the LE FV defined in Section III. Fig. 5 introduces the workflow of this proposed approach for a single convolutionnal layer. As a preliminary approach, we propose to encode only the first and second layers of a CNN. Indeed, for the deepest layers, the spatial dimension of the output are too small to extract a set of covariance matrices. The LE FV encoding can hence only be done for the first layers. Table 2 synthesizes the classification results obtained on the first (Conv 1) and second (Conv 2) layers of the vgg-verydeep-16 model [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF]. As observed, a gain is recorded for the proposed LE FV compared to the conventional FV approach. This is in agreement with the previous experiment on SIFT features where a similar conclusion has been done when encoding handcrafted features. Nevertheless, note that for this approach, the exploitation of the mean vector in the augmented SPD matrix (LE FV augmented) seems useless.

B. Global hybrid deep learning architecture

Now that LE FV have shown promising results to encode the first layers of a CNN. We propose an hybrid architecture which combines these LE FV with FV computed on the last layers of the CNN. The general framework is described in Fig. 6. Table 3 summarizes the classification results obtained for the LE FV encoding of SIFT and CNN descriptors.

As observed on this experiment on the UC Merced database, the combination of LE FV computed on the first two layers and FV computed on the last five CNN layers as shown in Fig. 6 allows to improve the classification performance (94.4 ± 0.1%) and exceeds the classification results obtained with the SIFT descriptors (79.4 ± 1.3%). A significant gain of 15% is observed.

VI. CONCLUSION

In this paper, an image classification algorithm has been introduced. It consists in encoding a set of local covariance matrices with Fisher vectors (FV) derived with the log-Euclidean metric: the log-Euclidean Fisher vectors (LE FV). An extension of this method to full local Gaussian descriptors has been proposed. It consists in computing the LE FV on augmented symmetric positive definite matrices gathering both the local mean vectors and local covariance matrices. The experiment on the UC Merced land use land cover dataset have shown the potential of the proposed approach compared to FV for the encoding of handcrafted features (such as SIFT) or convolutional neural networks features.

Fig. 1 .

 1 Fig. 1. Workflow of the general process : SIFT features coding for image classification.

3 )

 3 Codebook creation: A codebook (also named dictionary) is generated with the previously extracted descriptors computed on the training set. It consists in extracting a set of visual words which are classically obtained by a clustering algorithms, such as k-means or expectationmaximization (EM) algorithms. Formally, a Gaussian mixture model (GMM) is assumed to model the set (x 1 , x 2 , . . . , x T ) ∈ R T ×d of d-dimensional local features extracted from the training images (with d = 128 for the SIFT descriptors). The probability density function of the GMM model is given by:

  space of d × d symmetric positive definite matrices. In addition, the covariance matrix is assumed to be diagonal, i.e. σ 2 k = diag(Σ k ) ∈ R d is the variance vector. For a GMM model, a k-means or EM algorithm can be employed to estimate the parameters of each mixture component (µ k , σ 2 k and ω k ). These elements represent a codeword and the set composed by the K codewords gives the codebook. The k-means (resp. the EM) algorithm is used when the SIFT features are encoded with the VLAD (resp. the FV) descriptors. 4) Fisher vector and VLAD encoding: Let X = (x 1 , x 2 , . . . , x N ) be a set of d-dimensional vectors extracted form an image. The FV or VLAD encoding consists in projecting these descriptors in the previously learned codebook.

Fig. 2 .

 2 Fig. 2. Classification accuracy for the FV and VLAD encoding methods.

Fig. 2

 2 Fig. 2 draws the evolution of classification accuracy for the FV (in blue) and VLAD (in red) based encoding methods as a function of the proportion of training samples for K = 30.In addition, three versions of FV descriptors are considered, i.e. by considering separately the derivative with respect to the mean µ d k , the dispersion σ d k or by fusing them, noted respectively F V (µ), F V (σ) and F V (µ+σ). One can observe that best performances are obtained for the VLAD and FV (when both derivatives are considered) descriptors with a similar behavior. In the following, only FV descriptor will be used.

Fig. 3 .

 3 Fig. 3.Influence of the codebook dimension on the FV and LE FV classification accuracy.

Fig. 4 .

 4 Fig. 4.Influence of the number of retained principal components on classification accuracy for LE FV.

Table 1 .

 1 Comparison between FV and LE FV descriptors for K = 30 and N P CA = 20

Fig. 5 .

 5 Fig. 5. LE FV encoding for CNN features

Table 2 .

 2 Classification results for the first and second convolutional layers of vgg-verydeep-16 model and synthesis. Recently, some hybrid architectures have been proposed to combine FV and CNN in order to benefit from both approaches. For example, in[START_REF] Li | Integrating multilayer features of convolutional neural networks for remote sensing scene classification[END_REF], Li et al. have proposed an hybrid architecture which extract FV computed on the ouput of different convolutional layers of a pre-trained neural network. This strategy has shown competitive results for remote sensing image classification. The main idea consists in using multi-layer features of a pretrained CNN model. Once the features are extracted, improved FV encoding is applied to generate features vectors. Those vectors are then fused with features of fully-connected layers to represent the mid-level feature vectors of a scene image. Finally, a linear SVM classifier is applied for classification purpose.

	Descriptor	Conv 1	Conv 2
	FV [4]	58.2 ± 0.7%	62.5 ± 1.2%
	LE FV	70.3 ± 1.0%	87.7 ± 0.7%
	LE FV augmented	66.3 ± 1.1%	84.8 ± 0.2%
	as SIFT, an application to deep learning is introduced. Con-
	volutional Neural Networks (CNNs) have proven to be very
	effective in many image processing applications such as clas-
	sification, segmentation

Table 3 .

 3 Classification comparison between the two approaches comprising the LE FV encoding Descriptor Overall accuracy ± standard deviation SIFT 79.4 ± 1.3% CNN 94.4 ± 0.1%